Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Authors:
E. Hairer;S. P. Nørsett;G. Wanner
Affiliations:
Univ. de Gene`ve, Geneva, Switzerland;Univ. of Trondheim, Trondheim, Norway;Univ. de Gene`ve, Geneva, Switzerland
Venue:
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Year:
1993

Citing 0
Cited 557

Parallel program debugging with on-the-fly anomaly detection

Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods

ACM Transactions on Mathematical Software (TOMS)
Performance predictions for parallel diagonal-implicitly iterated Runge-Kutta methods

PADS '95 Proceedings of the ninth workshop on Parallel and distributed simulation
Fast and resolution independent line integral convolution

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++

ACM Transactions on Mathematical Software (TOMS)
Parallel ODE solvers

ICS '90 Proceedings of the 4th international conference on Supercomputing
A new high-order absolutely-stable explicit numerical integration algorithm for the time-domain simulation of nonlinear circuits

ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
On a High Order Numerical Method for Solving Partial Differential Equations in Complex Geometries

Journal of Scientific Computing
Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods

ACM Transactions on Mathematical Software (TOMS)
A coordination language for mixed task and and data parallel programs

Proceedings of the 1999 ACM symposium on Applied computing
A Transformation Approach to Derive Efficient Parallel Implementations

IEEE Transactions on Software Engineering - Special issue on architecture-independent languages and software tools parallel processing
Optimizing locality for ODE solvers

ICS '01 Proceedings of the 15th international conference on Supercomputing
Implementing Radau IIA methods for stiff delay differential equations

Computing
A fast implicit integration method for solving dynamic equations of movement

VRST '01 Proceedings of the ACM symposium on Virtual reality software and technology
Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

ACM Transactions on Mathematical Software (TOMS)
A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows

Journal of Scientific Computing
ORT: a communication library for orthogonal processor groups

Proceedings of the 2001 ACM/IEEE conference on Supercomputing
On the sensitivity analysis of the expected accumulated reward

Performance Evaluation
Analyzing the stability behaviour of solutions and their approximations in case of index-2 differential-algebraic systems

Mathematics of Computation
Differential algebraic equations with after-effect

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Explicit methods based on a class of four stage fourth order Runge-Kutta methods for preserving quadratic laws

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Boundedness and stability of solutions to difference equations

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Starting algorithms for low stage order RKN methods

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
T-Efficient Calculation of the ε-Solutions to Problems of Calculus and Applied Mathematics. II

Cybernetics and Systems Analysis
Component-Based Derivation of a Parallel Stiff ODE Solver Implemented in a Cluster of Computers

International Journal of Parallel Programming
Two Barriers on Strong-Stability-Preserving Time Discretization Methods

Journal of Scientific Computing
Fast Display of Illuminated Field Lines

IEEE Transactions on Visualization and Computer Graphics
Book News & Reviews

IEEE Computational Science & Engineering
A Fourth-Order Algorithm with Automatic Stepsize Control for the Transient Analysis of DSPNs

IEEE Transactions on Software Engineering
Optimized Runge-Kutta pairs for problems with oscillating solutions

Journal of Computational and Applied Mathematics
A multirate W-method for electrical networks in state-space formulation

Journal of Computational and Applied Mathematics
A collocation formulation of multistep methods for variable step-size extensions

Applied Numerical Mathematics
Stability in the numerical solution of the heat equation with nonlocal boundary conditions

Applied Numerical Mathematics
Blended implementation of block implicit methods for ODEs

Applied Numerical Mathematics
Post-projected Runge-Kutta methods for index-2 differential-algebriac equations

Applied Numerical Mathematics
Numerical behaviour of stable and unstable solitary waves

Applied Numerical Mathematics
Multiple shooting using a dichotomically stable integrator for solving differential-algebraic equations

Applied Numerical Mathematics
New methods for oscillatory problems based on classical codes

Applied Numerical Mathematics
Implementation of DIMSIMs for stiff differential systems

Applied Numerical Mathematics
A variable-stepsize variable-order multistep method for the integration of perturbed linear problems

Applied Numerical Mathematics
Algebraic conditions for high-order convergent deferred correction schemes based on Runge-Kutta-Nyström methods for second order boundary value problems

Applied Numerical Mathematics
Compensating for order variation in mesh refinement for direct transcription methods II: computational experience

Journal of Computational and Applied Mathematics
Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems

Journal of Computational and Applied Mathematics
Differential calculus for p-norms of complex-valued vector functions with applications

Journal of Computational and Applied Mathematics
Complexity of nonlinear two-point boundary-value problems

Journal of Complexity
Comparison of time and spatial collocation methods for the heat equation

Journal of Computational and Applied Mathematics
A composite Runge-Kutta method for the spectral solution of semilinear PDEs

Journal of Computational Physics
Attracting sets in index 2 differential algebraic equations and in their Runge-Kutta discretizations

Nonlinear Analysis: Theory, Methods & Applications
High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems

Applied Mathematics and Computation
Solving reduced chemical models in air pollution modelling

Applied Numerical Mathematics
Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems

Applied Numerical Mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations

Applied Numerical Mathematics
An embedded pair of exponentially fitted explicit Runge-Kutta methods

Journal of Computational and Applied Mathematics
An enhancement of transformation method

Applied Mathematics and Computation
Digital filters in adaptive time-stepping

ACM Transactions on Mathematical Software (TOMS)
An accelerated Poincaré-map method for autonomous oscillators

Applied Mathematics and Computation
Solving Orthogonal Matrix Differential Systems in Mathematica

ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Symplectic Methods for Separable Hamiltonian Systems

ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Two Step Runge-Kutta-Nyström Methods for y'' = f(x, y) and P-Stability

ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Stable Symplectic Integrators for Power Systems

ICCS '02 Proceedings of the International Conference on Computational Science-Part I
On Implementation of Vector Gauss Method for Solving Large-Scale Systems of Index 1 Differential-Algebraic Equations

ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Parallel Two-Step W-Methods on Singular Perturbation Problems

PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Pipelining for Locality Improvement in RK Methods

Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
A Class of Explicit Two-Step Runge-Kutta Methods with Enlarged Stability Regions for Parallel Computers

ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
Optimal Pruning in Parametric Differential Equations

CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Variable-Coefficient Difference Schemes for Quasilinear Evolution Problems

NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems

NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Construction of Seminumerical Schemes: Application to the Artificial Satellite Problem

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Variable Stepsizes in Symmetric Linear Multistep Methods

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A Numerical Comparison between Multi-revolution Algorithms for First-Order and Second-Order ODE Systems

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Sensitivity Analysis of the Expected Accumulated Reward Using Uniformization and IRK3 Methods

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Library support for hierarchical multi-processor tasks

Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods

Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
High-order schemes for conservative or dissipative systems

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Orthonormal integrators based on householder and givens transformations

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Increment formulations for rounding error reduction in the numerical solution of structured differential systems

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Computation of few Lyapunov exponents by geodesic based algorithms

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Designing a neural network via gradient flow

Second international workshop on Intelligent systems design and application
Aspects of a distributed solution of the Brusselator equation

PAS '95 Proceedings of the First Aizu International Symposium on Parallel Algorithms/Architecture Synthesis
A Fourth-Order Algorithm with Automatic Stepsize Control for the Transient Analysis of DSPNs

PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
ACETAF: A software package for computing validated bounds for Taylor coefficients of analytic functions

ACM Transactions on Mathematical Software (TOMS)
Interactive physically based solid dynamics

Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
QMC methods for the solution of delay differential equations

Journal of Computational and Applied Mathematics
Estimates of variable stepsize Runge--Kutta methods for sectorial evolution equations with nonsmooth data

Applied Numerical Mathematics
Extension and further development of the differential calculus for matrix norms with applications

Journal of Computational and Applied Mathematics
Geometric numerical integration applied to the elastic pendulum at higher-order resonance

Journal of Computational and Applied Mathematics
Construction of two-step Runge--Kutta methods with large regions of absolute stability

Journal of Computational and Applied Mathematics
An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

Journal of Computational Physics
A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Trigonometrically fitted predictor: corrector methods for IVPs with oscillating solutions

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
A high-order conservative Patankar-type discretisation for stiff systems of production-destruction equations

Applied Numerical Mathematics
B-convergence of general linear methods for stiff problems

Applied Numerical Mathematics
Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones

Mathematics of Computation
A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Mathematics of Computation
High-Quality Animation of 2D Steady Vector Fields

IEEE Transactions on Visualization and Computer Graphics
Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?

Journal of Computational and Applied Mathematics
Isospectral-like flows and eigenvalue problem

Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
On enumeration problems in Lie-Butcher theory

Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Four-step, two-stage, sixth-order, P-stable methods

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Energy conservative algorithm for numerical solution of ODES initial value problems

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Implicit extension of Taylor series method for initial value problems

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Variable step-size Störmer methods

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
A note on the selection of the step size in the variable step-size Störmer method

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
VS-VO Numerov method for the numerical solution of the Schrödinger equation

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Finite difference heterogeneous multi-scale method for homogenization problems

Journal of Computational Physics
The role of modeling in computational science education

Future Generation Computer Systems - Special issue: Selected papers from the workshop on education in computational sciences held at the ICCS 2002
Higher-order time integration schemes for the unsteady Navier--Stokes equations on unstructured meshes

Journal of Computational Physics
A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators

Journal of Computational and Applied Mathematics
An adaptive timestepping algorithm for stochastic differential equations

Journal of Computational and Applied Mathematics
Two-step error estimators for implicit Runge--Kutta methods applied to stiff systems

ACM Transactions on Mathematical Software (TOMS)
Performance optimization of RK methods using block-based pipelining

Performance analysis and grid computing
Multi-adaptive time integration

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
A variational splitting integrator for quantum molecular dynamics

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Semi-implicit projection methods for incompressible flow based on spectral deferred corrections

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Stability of linear multistep methods and applications to nonlinear parabolic problems

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Parallel 'Peer' two-step W-methods and their application to MOL-systems

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Stochastic differential algebraic equations of index 1 and applications in circuit simulation

Journal of Computational and Applied Mathematics
The BiM code for the numerical solution of ODEs

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
On implicit algorithms of continuation method with applications to dynamic systems

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
The visualization of myocardial strain for the improved analysis of cardiac mechanics

Proceedings of the 2nd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
High order Runge-Kutta-Nyström codes for the integration of oscillatory problems

Applied Numerical Mathematics
Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation

Applied Numerical Mathematics
The behaviour of the local error in splitting methods applied to stiff problems

Journal of Computational Physics
Exponentially fitted explicit Runge-Kutta-Nyström methods

Journal of Computational and Applied Mathematics
Noise Analysis for Optical Fiber Communication Systems

Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Pitching a baseball: tracking high-speed motion with multi-exposure images

ACM SIGGRAPH 2004 Papers
Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems

Computational Optimization and Applications
Are high order variable step equistage initializers better than standard starting algorithms?

Journal of Computational and Applied Mathematics
Preconditioned implicit solution of linear hyperbolic equations with adaptivity

Journal of Computational and Applied Mathematics
Adaptive stepsize based on control theory for stochastic differential equations

Journal of Computational and Applied Mathematics
Adaptive moving mesh computations for reaction--diffusion systems

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Runge-Kutta methods adapted to the numerical integration of oscillatory problems

Applied Numerical Mathematics
Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids

Applied Numerical Mathematics
Simply generated trees, B-series and Wigner processes

Random Structures & Algorithms
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics

Journal of Computational Physics
Non-Monte Carlo formulations and computational techniques for the stochastic non-linear Schrödinger equation

Journal of Computational Physics
Efficient solution of multi-term fractional differential equations using P(EC)mE methods

Computing
A Data-Re-Distribution Library for Multi-Processor Task Programming

IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 8 - Volume 09
On positive solutions in a phytoplankton-nutrient model

Journal of Computational and Applied Mathematics
An efficient solver for the high-order accurate time-discontinuous Galerkin (TDG) method for second-order hyperbolic systems

Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
An optimized Runge-Kutta method for the solution of orbital problems

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
A fourth algebraic order trignometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
A note on step-size selection in the Störmer-Cowell methods

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
On the stability of exponential fitting BDF algorithms

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Automatic Generation of Wave Digital Structures for Numerically Integrating Linear Symmetric Hyperbolic PDEs

Multidimensional Systems and Signal Processing
Parameter estimation and accuracy matching strategies for 2-D reactor models

Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Higher order regularity and approximation of solutions to the Monod biodegradation model

Applied Numerical Mathematics
An iterated pseudospectral method for delay partial differential equations

Applied Numerical Mathematics
Construction and Implementation of General Linear Methods for Ordinary Differential Equations: A Review

Journal of Scientific Computing
Important Aspects of Geometric Numerical Integration

Journal of Scientific Computing
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

Journal of Scientific Computing
Fourth-Order Runge---Kutta Schemes for Fluid Mechanics Applications

Journal of Scientific Computing
An A Priori Error Analysis of the hp-Version of the Continuous Galerkin FEM for Nonlinear Initial Value Problems

Journal of Scientific Computing
Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds

Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
On the application of partial evaluation to the optimisation of cardiac electrophysiological simulations

Proceedings of the 2006 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Space---Time Adaptive Solution of First Order PDES

Journal of Scientific Computing
A class of explicit two-step hybrid methods for second-order IVPs

Journal of Computational and Applied Mathematics
Computational approaches to parameter estimation and model selection in immunology

Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Pitfalls in fast numerical solvers for fractional differential equations

Journal of Computational and Applied Mathematics
Adaptive time-stepping and computational stability

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Evaluating numerical ODE/DAE methods, algorithms and software

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Time domain analog circuit simulation

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Stage value predictors for additive and partitioned Runge-Kutta methods

Applied Numerical Mathematics
Long-time error estimation for semi-linear parabolic equations

Journal of Computational and Applied Mathematics
Stability analysis of frequency and step length dependent Runge-Kutta-Nyström methods

Future Generation Computer Systems
A Fifth Order Flux Implicit WENO Method

Journal of Scientific Computing
Implicit Taylor methods for parabolic problems with nonsmooth data and applications to optimal heat control

Journal of Computational and Applied Mathematics
On the generation of P-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods

Journal of Computational and Applied Mathematics
One-step approximations for stochastic functional differential equations

Applied Numerical Mathematics
On error estimation in general linear methods for stiff ODEs

Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Software for ordinary and delay differential equations: accurate discrete approximate solutions are not enough

Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Numerical solution of a problem in the theory of epidemics

Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
A Matlab package for automatically generating Runge-Kutta trees, order conditions, and truncation error coefficients

ACM Transactions on Mathematical Software (TOMS)
Exponential fitting BDF algorithms: explicit and implicit 0-stable methods

Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Variable stepsize implementation of multistep methods for y''=f(x, y, y')

Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Adaptive stiff solvers at low accuracy and complexity

Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
Stage reduction on P-stable numerov type methods of eighth order

Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
Partitioning methods for reaction-diffusion problems

Applied Numerical Mathematics
Frequency evaluation for exponentially fitted Runge-Kutta methods

Journal of Computational and Applied Mathematics
New methods for oscillatory systems based on ARKN methods

Applied Numerical Mathematics
An integral equation method for epitaxial step-flow growth simulations

Journal of Computational Physics
N-body simulations: The performance of some integrators

ACM Transactions on Mathematical Software (TOMS)
A note on symplecticity of step-transition mappings for multi-step methods

Journal of Computational and Applied Mathematics
Complexity of initial-value problems for ordinary differential equations of order k

Journal of Complexity
Nordsieck methods on nonuniform grids: stability and order reduction phenomenon

Mathematics and Computers in Simulation
Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Linearly implicit Runge-Kutta methods and approximate matrix factorization

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Stability regions of one step mixed collocation methods for y" = f (x, y)

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Convergence of Runge-Kutta methods applied to linear partial differential-algebraic equations

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Stepsize restrictions for total-variation-boundedness in general Runge-Kutta procedures

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
On the Newton iteration in the application of collocation methods to implicit delay equations

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
A survey of shadowing methods for numerical solutions of ordinary differential equations

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
On the positivity step size threshold of Runge-Kutta methods

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Runge-Kutta-Nyström methods with maximized stability domain in structural dynamics

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Numerical analysis of structure preserving Nyström methods for Hamiltonian systems

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Rosenbrock-type 'Peer' two-step methods

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Multi time scale differential equations for simulating frequency modulated signals

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Perturbation index of linear partial differential-algebraic equations

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
A charge oriented mixed multirate method for a special class of index-1 network equations in chip design

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain

Journal of Computational Physics
A parallel explicit/implicit time stepping scheme on block-adaptive grids

Journal of Computational Physics
Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations

Journal of Computational and Applied Mathematics
A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators

Applied Numerical Mathematics
Optimized high-order finite difference wave equations modeling on reconfigurable computing platform

Microprocessors & Microsystems
Extended Runge-Kutta-like formulae

Applied Numerical Mathematics
Conjugate symplecticity of second-order linear multi-step methods

Journal of Computational and Applied Mathematics
Parameter range reduction for ODE models using cumulative backward differentiation formulas

Journal of Computational and Applied Mathematics
Analysis of trigonometric implicit Runge-Kutta methods

Journal of Computational and Applied Mathematics
A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems

Applied Numerical Mathematics
Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s

Journal of Computational and Applied Mathematics
A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations

Journal of Computational and Applied Mathematics
Improving locality for ODE solvers by program transformations

Scientific Programming
Input-to-state stability of Runge-Kutta methods for nonlinear control systems

Journal of Computational and Applied Mathematics
Constant coefficient linear multistep methods with step density control

Journal of Computational and Applied Mathematics
Design of software for ODEs

Journal of Computational and Applied Mathematics
Derivation of continuous explicit two-step Runge-Kutta methods of order three

Journal of Computational and Applied Mathematics
Blended implicit methods for solving ODE and DAE problems, and their extension for second-order problems

Journal of Computational and Applied Mathematics
New numerical integrators based on solvability and splitting

Journal of Computational and Applied Mathematics
Computing statistics for Hamiltonian systems: A case study

Journal of Computational and Applied Mathematics
Space-time adaptive finite difference method for European multi-asset options

Computers & Mathematics with Applications
An explicit Numerov-type method for second-order differential equations with oscillating solutions

Computers & Mathematics with Applications
An Adaptive Multimeme Algorithm for Designing HIV Multidrug Therapies

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Comparing Synchronous and Asynchronous Variable Step Size Explicit ODE Solvers: A Simulation Study

Proceedings of the 21st International Workshop on Principles of Advanced and Distributed Simulation
Formal Validation of Asynchronous Interaction-Agents Algorithms for Reaction-Diffusion Problems

Proceedings of the 21st International Workshop on Principles of Advanced and Distributed Simulation
A new adaptive Runge-Kutta method for stochastic differential equations

Journal of Computational and Applied Mathematics
An adaptive finite element method for magnetohydrodynamics

Journal of Computational Physics
Interfacial dynamics in Stokes flow via a three-dimensional fully-implicit interfacial spectral boundary element algorithm

Journal of Computational Physics
Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

Journal of Computational Physics
Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs

Applied Numerical Mathematics
Numerical methods for the eigenvalue determination of second-order ordinary differential equations

Journal of Computational and Applied Mathematics
Numerical methods for ordinary differential equations on matrix manifolds

Journal of Computational and Applied Mathematics
Hybrid method for the chemical master equation

Journal of Computational Physics
Accuracy analysis of acceleration schemes for stiff multiscale problems

Journal of Computational and Applied Mathematics
Stability of IMEX Runge-Kutta methods for delay differential equations

Journal of Computational and Applied Mathematics
Statistical mechanics of Arakawa's discretizations

Journal of Computational Physics
Error propagation of general linear methods for ordinary differential equations

Journal of Complexity
Mean-square convergence of stochastic multi-step methods with variable step-size

Journal of Computational and Applied Mathematics
Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation

Journal of Computational Physics
Solution of the matrix eigenvalue problem VA+A*V=µV with applications to the study of free linear dynamical systems

Journal of Computational and Applied Mathematics
Letter to the Editor: Enumeration results for Runge-Kutta methods for index 2 DAEs

Journal of Computational and Applied Mathematics
Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs

Applied Numerical Mathematics
Explicit two-step peer methods

Computers & Mathematics with Applications
Second-order implicit-explicit scheme for the Gray-Scott model

Journal of Computational and Applied Mathematics
Some secant approximations for Rosenbrock W-methods

Applied Numerical Mathematics
Enhanced order composition methods

Applied Numerical Mathematics
Efficient computation of characteristic roots of delay differential equations using LMS methods

Journal of Computational and Applied Mathematics
Continuous weak approximation for stochastic differential equations

Journal of Computational and Applied Mathematics
Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations

Mathematics and Computers in Simulation
Algorithm 874: BACOLR—spatial and temporal error control software for PDEs based on high-order adaptive collocation

ACM Transactions on Mathematical Software (TOMS)
Musculotendon simulation for hand animation

ACM SIGGRAPH 2008 papers
Solution of a class of Riccati equations

MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
Contaminant transport with groundwater flow in unconfined aquifer: two-dimensional numerical solution

SMO'06 Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization
Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration

Journal of Computational Physics
Mixed task and data parallel executions in general linear methods

Scientific Programming
Symbolic derivation of order conditions for hybrid Numerov-type methods solving y˝=f(x,y)

Journal of Computational and Applied Mathematics
Convergence analysis of the Levenberg-Marquardt method

Optimization Methods & Software
New upper bounds for excited vibration systems with applications of the differential calculus of norms

International Journal of Computer Mathematics
Stability analysis of the BDF Slowest-first multirate methods

International Journal of Computer Mathematics - Splitting Methods for Differential Equations
A class of three-point spline collocation methods for solving delay differential equations

International Journal of Computer Mathematics
Error analysis of Parallel Multivalue Hybrid Methods for index-2 Differential-Algebraic Equations

International Journal of Computing Science and Mathematics
Asymptotic stability of numerical methods for linear delay parabolic differential equations

Computers & Mathematics with Applications
Trigonometrically-fitted ARKN methods for perturbed oscillators

Applied Numerical Mathematics
Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations

Journal of Computational and Applied Mathematics
Object-Oriented Implementation of Software for Solving Ordinary Differential Equations

Scientific Programming - The First Annual Object-Oriented Numerics Conference (OON-SKI '93)
Taylor series method with numerical derivatives for initial value problems

Journal of Computational Methods in Sciences and Engineering - Computational and Mathematical Methods for Science and Engineering Conference 2002 - CMMSE-2002
Implicit extension of taylor series method for initial value problems

Journal of Computational Methods in Sciences and Engineering
Twostep-by-twostep PIRK-type PC methods with continuous output formulas

Journal of Computational and Applied Mathematics
Acceleration of lattice Boltzmann models through state extrapolation: a reaction--diffusion example

Applied Numerical Mathematics
Strong stability of singly-diagonally-implicit Runge--Kutta methods

Applied Numerical Mathematics
Numerical Tests with Gauss-Type Nested Implicit Runge-Kutta Formulas

ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Collocation---Based Two Step Runge---Kutta Methods for Ordinary Differential Equations

ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
Communicating Multiprocessor-Tasks

Languages and Compilers for Parallel Computing
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform

Journal of Computational and Applied Mathematics
Improved radial basis function methods for multi-dimensional option pricing

Journal of Computational and Applied Mathematics
Numerical volume preservation of a divergence free fluid under symmetry

Applied Numerical Mathematics
Eulerian-Lagrangian time-stepping methods for convection-dominated problems

International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

Journal of Computational and Applied Mathematics
Functionally fitted explicit pseudo two-step Runge--Kutta methods

Applied Numerical Mathematics
Adaptive solution of the master equation in low dimensions

Applied Numerical Mathematics
Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery

Mathematics and Computers in Simulation
Optimal implicit strong stability preserving Runge--Kutta methods

Applied Numerical Mathematics
Superconvergent explicit two-step peer methods

Journal of Computational and Applied Mathematics
Scheifele two-step methods for perturbed oscillators

Journal of Computational and Applied Mathematics
SVD algorithms to approximate spectra of dynamical systems

Mathematics and Computers in Simulation
KINSOLVER: A simulator for computing large ensembles of biochemical and gene regulatory networks

Computers & Mathematics with Applications
Multirate Explicit Adams Methods for Time Integration of Conservation Laws

Journal of Scientific Computing
Extrapolation discontinuous Galerkin method for ultraparabolic equations

Journal of Computational and Applied Mathematics
On quasi-consistent integration by Nordsieck methods

Journal of Computational and Applied Mathematics
Wavelet-based adaptive grids for multirate partial differential-algebraic equations

Applied Numerical Mathematics
Recent advances in linear analysis of convergence for splittings for solving ODE problems

Applied Numerical Mathematics
A parametrization method for the numerical solution of singular differential equations

Applied Numerical Mathematics
Analysis of a multirate theta-method for stiff ODEs

Applied Numerical Mathematics
A multirate ROW-scheme for index-1 network equations

Applied Numerical Mathematics
Adaptive nested implicit Runge--Kutta formulas of Gauss type

Applied Numerical Mathematics
Parameter optimization for explicit parallel peer two-step methods

Applied Numerical Mathematics
A New Class of Highly Accurate Solvers for Ordinary Differential Equations

Journal of Scientific Computing
A robust trigonometrically fitted embedded pair for perturbed oscillators

Journal of Computational and Applied Mathematics
Solving Ordinary Differential Equations by Simplex Integrals

Numerical Analysis and Its Applications
On a class of spline-collocation methods for solving second-order initial-value problems

International Journal of Computer Mathematics
Strong stability preserving hybrid methods

Applied Numerical Mathematics
Accuracy and linear stability of RKN methods for solving second-order stiff problems

Applied Numerical Mathematics
General error propagation in the RKrGLm method

Journal of Computational and Applied Mathematics
On an accurate third order implicit-explicit Runge--Kutta method for stiff problems

Applied Numerical Mathematics
Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis

Applied Numerical Mathematics
A Parallel Combustion Solver within an Operator Splitting Context for Engine Simulations on Grids

Large-Scale Scientific Computing
Runge-Kutta Schemes in Control Constrained Optimal Control

Large-Scale Scientific Computing
Comparison of TKSL to world standards

International Journal of Autonomic Computing
Parallel two-step ROW-methods for stiff delay differential equations

Applied Numerical Mathematics
A Parallel Algorithm To Solve Large Stiff ODE Systems On Grid Systems

International Journal of High Performance Computing Applications
An implicit Landweber method for nonlinear ill-posed operator equations

Journal of Computational and Applied Mathematics
Space--time adaptive multiresolution methods for hyperbolic conservation laws: Applications to compressible Euler equations

Applied Numerical Mathematics
The adaptive operational Tau method for systems of ODEs

Journal of Computational and Applied Mathematics
Constraint Reasoning for Differential Models

Proceedings of the 2005 conference on Constraint Reasoning for Differential Models
Stability of central finite difference schemes on non-uniform grids for the Black--Scholes equation

Applied Numerical Mathematics
Sliding Window Abstraction for Infinite Markov Chains

CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems

Journal of Scientific Computing
Static Analysis of Concurrent Programs Using Ordinary Differential Equations

ICTAC '09 Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing
Multisymplecticity and wave action conservation

Mathematics and Computers in Simulation
The fully implicit stochastic-α method for stiff stochastic differential equations

Journal of Computational Physics
Polynomial chaos for simulating random volatilities

Mathematics and Computers in Simulation
Numerical smoothing of Runge-Kutta schemes

Journal of Computational and Applied Mathematics
A constraint satisfaction approach to parametric differential equations

IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
One-step approximations for stochastic functional differential equations

Applied Numerical Mathematics
Stage value predictors for additive and partitioned Runge--Kutta methods

Applied Numerical Mathematics
Higher order regularity and approximation of solutions to the Monod biodegradation model

Applied Numerical Mathematics
An iterated pseudospectral method for delay partial differential equations

Applied Numerical Mathematics
Nordsieck representation of two-step Runge--Kutta methods for ordinary differential equations

Applied Numerical Mathematics
Stability regions of one step mixed collocation methods for y″=f(x,y)

Applied Numerical Mathematics
Stepsize restrictions for total-variation-boundedness in general Runge--Kutta procedures

Applied Numerical Mathematics
A survey of shadowing methods for numerical solutions of ordinary differential equations

Applied Numerical Mathematics
Runge--Kutta--Nyström methods with maximized stability domain in structural dynamics

Applied Numerical Mathematics
Numerical analysis of structure preserving Nyström methods for Hamiltonian systems

Applied Numerical Mathematics
A charge oriented mixed multirate method for a special class of index-1 network equations in chip design

Applied Numerical Mathematics
On error estimation in general linear methods for stiff ODEs

Applied Numerical Mathematics
Software for ordinary and delay differential equations: Accurate discrete approximate solutions are not enough

Applied Numerical Mathematics
Numerical solution of a problem in the theory of epidemics

Applied Numerical Mathematics
Prediction of a Lorenz chaotic attractor using two-layer perceptron neural network

Applied Soft Computing
Scalable computing with parallel tasks

Proceedings of the 2nd Workshop on Many-Task Computing on Grids and Supercomputers
Technical section: Implementation of a method of curved ray tracing for inhomogeneous atmospheres

Computers and Graphics
Scalable computation of streamlines on very large datasets

Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
An adaptive algorithm for simulation of stochastic reaction-diffusion processes

Journal of Computational Physics
High-order W-methods

Journal of Computational and Applied Mathematics
A self-learning framework for services selection

International Journal of Information Technology and Management
Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations

Computers and Structures
The quantum square well with moving boundaries: A numerical analysis

Computers & Mathematics with Applications
Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation

Journal of Computational and Applied Mathematics
A variable step implicit block multistep method for solving first-order ODEs

Journal of Computational and Applied Mathematics
An efficient solver for the high-order accurate time-discontinuous Galerkin (TDG) method for second-order hyperbolic systems

Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Finite difference methods for second order in space, first order in time hyperbolic systems and the linear shifted wave equation as a model problem in numerical relativity

Journal of Computational Physics
Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds

Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Computational approaches to parameter estimation and model selection in immunology

Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Frequency evaluation for exponentially fitted Runge-Kutta methods

Journal of Computational and Applied Mathematics
Order reduction and how to avoid it when explicit Runge-Kutta-Nyström methods are used to solve linear partial differential equations

Journal of Computational and Applied Mathematics
A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
On the stability of exponential fitting BDF algorithms

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
A note on step-size selection in the Störmer-Cowell methods

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
An optimized Runge-Kutta method for the solution of orbital problems

Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Adaptive time-stepping and computational stability

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Evaluating numerical ODE/DAE methods, algorithms and software

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Time domain analog circuit simulation

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
A class of explicit two-step hybrid methods for second-order IVPs

Journal of Computational and Applied Mathematics
Implicit Taylor methods for parabolic problems with nonsmooth data and applications to optimal heat control

Journal of Computational and Applied Mathematics
Pitfalls in fast numerical solvers for fractional differential equations

Journal of Computational and Applied Mathematics
On the generation of P-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods

Journal of Computational and Applied Mathematics
Initializers for RK-Gauss methods based on pseudo-symplecticity

Journal of Computational and Applied Mathematics
Efficient iterations for Gauss methods on second-order problems

Journal of Computational and Applied Mathematics
Blended implicit methods for the numerical solution of DAE problems

Journal of Computational and Applied Mathematics
Some new additive Runge-Kutta methods and their applications

Journal of Computational and Applied Mathematics
Stepsize selection for ordinary differential equations

ACM Transactions on Mathematical Software (TOMS)
BDF-like methods for nonlinear dynamic analysis

Journal of Computational Physics
A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11

Journal of Computational and Applied Mathematics
Direct time integration algorithm with controllable numerical dissipation for structural dynamics: Two-step Lambda method

Applied Numerical Mathematics
New embedded explicit pairs of exponentially fitted Runge-Kutta methods

Journal of Computational and Applied Mathematics
A hybrid Finite Integration-Finite Volume Scheme

Journal of Computational Physics
A 17th-order Radau IIA method for package RADAU. Applications in mechanical systems

Computers & Mathematics with Applications
Computational aspects of chemical data assimilation into atmospheric models

ICCS'03 Proceedings of the 2003 international conference on Computational science
Extrapolated multistep methods and local-global step size control

ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. Part I: Stability and order results

Journal of Computational and Applied Mathematics
On proving the absence of oscillations in models of genetic circuits

AB'07 Proceedings of the 2nd international conference on Algebraic biology
Co-simulation of distributed embedded real-time control systems

IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Partial approximation of the master equation by the Fokker-Planck equation

PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
A survey of interval Runge-Kutta and multistep methods for solving the initial value problem

PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Abstract interpretation of the physical inputs of embedded programs

VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Novel generalized-α methods for interfield parallel integration of heterogeneous structural dynamic systems

Journal of Computational and Applied Mathematics
Numerical treatment of oscillatory functional differential equations

Journal of Computational and Applied Mathematics
Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag

Journal of Computational and Applied Mathematics
A Code Based on the Two-Stage Runge-Kutta Gauss Formula for Second-Order Initial Value Problems

ACM Transactions on Mathematical Software (TOMS)
Error propagation in numerical approximations near relative equilibria

Journal of Computational and Applied Mathematics
A comparison of high-order time integrators for thermal convection in rotating spherical shells

Journal of Computational Physics
New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation

Computers & Mathematics with Applications
Contribution of the delay differential equations to the complex economic macrodynamics

WSEAS TRANSACTIONS on SYSTEMS
Asymptotic stability of block boundary value methods for delay differential-algebraic equations

Mathematics and Computers in Simulation
An efficient local time-stepping scheme for solution of nonlinear conservation laws

Journal of Computational Physics
Generalized delay differential equations to economic dynamics and control

AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
A new diagonally implicit Runge-Kutta-Nyström method for periodic IVPs

WSEAS Transactions on Mathematics
Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

Advances in Computational Mathematics
A variable step-size control algorithm for the weak approximation of stochastic differential equations

Numerical Algorithms
An efficient error control mechanism for the adaptive 'parareal' time discretization algorithm

SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Review: On the fractional signals and systems

Signal Processing
Including ordinary differential equations based constraints in the standard CP framework

CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Source-to-source optimization of CUDA C for GPU accelerated cardiac cell modeling

EuroPar'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part I
Stein implicit Runge-Kutta methods with high stage order for large-scale ordinary differential equations

Applied Numerical Mathematics
Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway

Computer Methods and Programs in Biomedicine
On the derivation of explicit two-step peer methods

Applied Numerical Mathematics
A numerical ODE solver that preserves the fixed points and their stability

Journal of Computational and Applied Mathematics
Comparison of some Lie-symmetry-based integrators

Journal of Computational Physics
Original article: Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations

Mathematics and Computers in Simulation
Applying ordinary differential equations to the performance analysis of service composition

ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
Specialized sparse matrices solver in the chemical part of an environmental model

NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Runge-Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations

SIAM Journal on Numerical Analysis
A Stable Multistep Scheme for Solving Backward Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Continuous Block $\theta$-Methods for Ordinary and Delay Differential Equations

SIAM Journal on Scientific Computing
Extrapolated Implicit-Explicit Time Stepping

SIAM Journal on Scientific Computing
Continuous and Discrete Composite Adjoints for the Hessian of the Lagrangian in Shooting Algorithms for Dynamic Optimization

SIAM Journal on Scientific Computing
New Algorithms for Optimal Online Checkpointing

SIAM Journal on Scientific Computing
Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control

SIAM Journal on Scientific Computing
Stochastic Runge-Kutta Methods for Itô SODEs with Small Noise

SIAM Journal on Scientific Computing
Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions

SIAM Journal on Scientific Computing
Optimal Explicit Strong-Stability-Preserving General Linear Methods

SIAM Journal on Scientific Computing
Dynamic selection of implementation variants of sequential iterated runge-kutta methods with tile size sampling

Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Symplectic exponentially-fitted four-stage Runge---Kutta methods of the Gauss type

Numerical Algorithms
Encoding the fine-structured mechanism of action potential dynamics with qualitative motifs

Journal of Computational Neuroscience
Original article: Construction and implementation of highly stable two-step continuous methods for stiff differential systems

Mathematics and Computers in Simulation
Speed versus stability of multi-rate Runge-Kutta methods in transient electronic circuit simulation

ICOSSSE'05 Proceedings of the 4th WSEAS/IASME international conference on System science and simulation in engineering
Graphical simulation environments for modelling and simulation of integrative physiology

Computer Methods and Programs in Biomedicine
Jacobi alternative to Bayesian evidence maximization in diffusion filtering

ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
On the order of deferred correction

Applied Numerical Mathematics
On the simulation of nonlinear bidimensional spiking neuron models

Neural Computation
Experimental validation of high-order time integration for non-linear heat transfer problems

Computational Mechanics
Original article: Error growth in the numerical integration of periodic orbits

Mathematics and Computers in Simulation
Shooting methods for a PT-symmetric periodic eigenvalue problem

Numerical Algorithms
A class of collocation methods for numerical integration of initial value problems

Computers & Mathematics with Applications
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)

Journal of Computational Physics
Error Analysis for hp-FEM Semi-Lagrangian Second Order BDF Method for Convection-Dominated Diffusion Problems

Journal of Scientific Computing
Component-based programming techniques for coarse-grained parallelism

Proceedings of the 19th High Performance Computing Symposia
FATODE: a library for forward, adjoint and tangent linear integration of stiff systems

Proceedings of the 19th High Performance Computing Symposia
Continuous block implicit hybrid one-step methods for ordinary and delay differential equations

Applied Numerical Mathematics
Runge-Kutta methods for jump-diffusion differential equations

Journal of Computational and Applied Mathematics
Global error estimation and control in linearly-implicit parallel two-step peer W-methods

Journal of Computational and Applied Mathematics
A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

Journal of Computational Physics
Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems

SIAM Journal on Numerical Analysis
Linear Stability of Partitioned Runge-Kutta Methods

SIAM Journal on Numerical Analysis
Partitioned Runge-Kutta-Chebyshev Methods for Diffusion-Advection-Reaction Problems

SIAM Journal on Scientific Computing
Combining measures for temporal and spatial locality

ISPA'06 Proceedings of the 2006 international conference on Frontiers of High Performance Computing and Networking
Reaction-agents: first mathematical validation of a multi-agent system for dynamical biochemical kinetics

EPIA'05 Proceedings of the 12th Portuguese conference on Progress in Artificial Intelligence
Forward, tangent linear, and adjoint runge-kutta methods in KPP–2.2

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
On the properties of runge-kutta discrete adjoints

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Symmetric runge-kutta methods with higher derivatives and quadratic extrapolation

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
On a family of cheap symmetric one-step methods of order four

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Derivation of Strictly Stable High Order Difference Approximations for Variable-Coefficient PDE

Journal of Scientific Computing
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

Journal of Scientific Computing
Applicability of load balancing strategies to data-parallel embedded runge-kutta integrators

Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Simulation-based analysis of parallel runge-kutta solvers

PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Quantized state simulation of spiking neural networks

Simulation
The implicit midpoint rule for a class of convex differential inclusions

LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Adjoint computations in data assimilation problems using a 4-stage rosenbrock method

LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I: The linear case

Journal of Computational and Applied Mathematics
Comparative analysis of solution methods for delay differential equations in hematology

LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Convergence of adaptive BEM for some mixed boundary value problem

Applied Numerical Mathematics
On stable integration of stiff ordinary differential equations with global error control

ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
An algorithm for second order initial and boundary value problems with an automatic error estimate based on a third derivative method

Numerical Algorithms
Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics

Journal of Computational Physics
Algorithm 919: A Krylov Subspace Algorithm for Evaluating the ϕ-Functions Appearing in Exponential Integrators

ACM Transactions on Mathematical Software (TOMS)
MABSys: modeling and analysis of biological systems

ANB'10 Proceedings of the 4th international conference on Algebraic and Numeric Biology
Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks

Journal of Computational Neuroscience
Explicit Nordsieck methods with quadratic stability

Numerical Algorithms
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side

Journal of Computational and Applied Mathematics
An operational semantics for Simulink's simulation engine

Proceedings of the 13th ACM SIGPLAN/SIGBED International Conference on Languages, Compilers, Tools and Theory for Embedded Systems
Ocean modelling for climate studies: Eliminating short time scales in long-term, high-resolution studies of ocean circulation

Mathematical and Computer Modelling: An International Journal
A 5(3) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems

Mathematical and Computer Modelling: An International Journal
Performance of perturbation methods on orbit prediction

Mathematical and Computer Modelling: An International Journal
A new family of exponentially fitted methods

Mathematical and Computer Modelling: An International Journal
A class of ergodic solutions of nonlinear differential equations and numerical treatment

Mathematical and Computer Modelling: An International Journal
Construction of explicit runge-kutta pairs with stiffness detection

Mathematical and Computer Modelling: An International Journal
Trigonometrically fitted fifth-order runge-kutta methods for the numerical solution of the schrödinger equation

Mathematical and Computer Modelling: An International Journal
A fifth algebraic order trigonometrically-fitted modified runge-kutta zonneveld method for the numerical solution of orbital problems

Mathematical and Computer Modelling: An International Journal
Legendre-Gauss-Radau Collocation Method for Solving Initial Value Problems of First Order Ordinary Differential Equations

Journal of Scientific Computing
Convergence on error correction methods for solving initial value problems

Journal of Computational and Applied Mathematics
Illustrative Membrane Clipping

Computer Graphics Forum
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems

Journal of Computational Physics
Global Error Control in Adaptive Nordsieck Methods

SIAM Journal on Scientific Computing
Regularizing properties of difference schemes for singular integral-differential equations

Applied Numerical Mathematics
Two-step modified collocation methods with structured coefficient matrices

Applied Numerical Mathematics
An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. Part II: Convergence results

Applied Numerical Mathematics
Search for highly stable two-step Runge-Kutta methods

Applied Numerical Mathematics
Linearly implicit peer methods for the compressible Euler equations

Applied Numerical Mathematics
Numerical aspects in the dynamic simulation of geometrically exact rods

Applied Numerical Mathematics
A variable time-step-size code for advection-diffusion-reaction PDEs

Applied Numerical Mathematics
Stabilized overlapping modular time integration of coupled differential-algebraic equations

Applied Numerical Mathematics
Convergence of continuous approximations for discontinuous ODEs

Applied Numerical Mathematics
Spatial simulation of pushbelt CVTs with time-stepping schemes

Applied Numerical Mathematics
On algebraic stability of general linear methods and peer methods

Applied Numerical Mathematics
Peer methods for the one-dimensional shallow-water equations with CWENO space discretization

Applied Numerical Mathematics
Quasistatic approximations for stiff second order differential equations

Applied Numerical Mathematics
Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control

Applied Numerical Mathematics
Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts

Applied Numerical Mathematics
Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations

Journal of Computational Physics
Symmetric partitioned Runge-Kutta methods for differential equations on Lie groups

Applied Numerical Mathematics
A stiffly accurate Rosenbrock-type method of order 2 applied to FE-analyses in finite strain viscoelasticity

Applied Numerical Mathematics
Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations

Applied Numerical Mathematics
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS

ACM Transactions on Mathematical Software (TOMS)
Efficient implementation of the hybrid method for stochastic simulation of biochemical systems

Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Development of Java multi-threaded simulation for chemical reacting flow of ethanol

Advances in Engineering Software
Convergence of the forward-backward sweep method in optimal control

Computational Optimization and Applications
Geometric Breathers of the mKdV Equation

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
General linear methods for y˝=f(y(t))

Numerical Algorithms
High-order explicit local time-stepping methods for damped wave equations

Journal of Computational and Applied Mathematics
Numerical search for algebraically stable two-step almost collocation methods

Journal of Computational and Applied Mathematics
Numerical simulation of the impact and deposition of charged particulate droplets

Journal of Computational Physics
Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations

Applied Numerical Mathematics
The existence of stepsize-coefficients for boundedness of linear multistep methods

Applied Numerical Mathematics
A stepsize control algorithm for SDEs with small noise based on stochastic Runge---Kutta Maruyama methods

Numerical Algorithms
Locality improvement of data-parallel Adams-Bashforth methods through block-based pipelining of time steps

Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Programming support and scheduling for communicating parallel tasks

Journal of Parallel and Distributed Computing
Energy-scale aware feature extraction for flow visualization

EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
High order explicit Runge---Kutta Nyström pairs

Numerical Algorithms
Exponential Taylor methods: Analysis and implementation

Computers & Mathematics with Applications
High-order symmetric multistep cosine methods

Applied Numerical Mathematics
Adapted Falkner-type methods solving oscillatory second-order differential equations

Numerical Algorithms
PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Journal of Computational Physics
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales

Journal of Scientific Computing
Numerical simulation of shear layer instability using a scheme with ninth-order multioperator approximations

Computational Mathematics and Mathematical Physics
Solving delay differential equations in S-ADAPT by method of steps

Computer Methods and Programs in Biomedicine
High-order quasi-static finite element computations in space and time with application to finite strain viscoelasticity

Computers & Mathematics with Applications
Viewpoints, formalisms, languages, and tools for cyber-physical systems

Proceedings of the 6th International Workshop on Multi-Paradigm Modeling
Repeated spatial extrapolation: An extraordinarily efficient approach for option pricing

Journal of Computational and Applied Mathematics
Strongly A-stable first stage explicit collocation methods with stepsize control for stiff and differential-algebraic equations

Journal of Computational and Applied Mathematics
Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations

Applied Numerical Mathematics
Direct integrators of Runge-Kutta type for special third-order ordinary differential equations

Applied Numerical Mathematics
An efficient algorithm for computing the dynamic responses of one-dimensional periodic structures and periodic structures with defects

Computational Mechanics
Implications of order reduction for implicit Runge-Kutta methods

Numerical Algorithms
Original article: Symmetric and symplectic exponentially fitted Runge-Kutta-Nyström methods for Hamiltonian problems

Mathematics and Computers in Simulation
Original article: On the numerical and computational aspects of non-smoothnesses that occur in railway vehicle dynamics

Mathematics and Computers in Simulation
Original article: Numerical computation of derivatives in systems of delay differential equations

Mathematics and Computers in Simulation
High accuracy solutions to energy gradient flows from material science models

Journal of Computational Physics
Application of a shock-fitted spectral collocation method for computing transient high-speed inviscid flows over a blunt nose

Journal of Computational Physics
Special extended Nyström tree theory for ERKN methods

Journal of Computational and Applied Mathematics
Efficient integration of strangeness-free non-stiff differential-algebraic equations by half-explicit methods

Journal of Computational and Applied Mathematics
Projector based integration of DAEs with the Taylor series method using automatic differentiation

Journal of Computational and Applied Mathematics
Adaptive ODE solvers in extended Kalman filtering algorithms

Journal of Computational and Applied Mathematics
Local and global error estimation and control within explicit two-step peer triples

Journal of Computational and Applied Mathematics
A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems

Journal of Computational and Applied Mathematics
Rosenbrock-type methods with Inexact AMF for the time integration of advection-diffusion-reaction PDEs

Journal of Computational and Applied Mathematics
A stabilization of multistep linearly implicit schemes for dissipative systems

Journal of Computational and Applied Mathematics
Discretization of the Wave Equation Using Continuous Elements in Time and a Hybridizable Discontinuous Galerkin Method in Space

Journal of Scientific Computing
Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells

Journal of Computational Physics
Combined scheduling and mapping for scalable computing with parallel tasks

Scientific Programming - Biological Knowledge Discovery and Data Mining
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation, Part I: Template-based generic programming

Scientific Programming - A New Overview of the Trilinos Project --Part 1
Asymptotic solvers for second-order differential equation systems with multiple frequencies

Calcolo: a quarterly on numerical analysis and theory of computation
EASY-FIT: a software system for data fitting in dynamical systems

Structural and Multidisciplinary Optimization
Extrapolation-based implicit-explicit general linear methods

Numerical Algorithms
A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems

Numerical Algorithms
Error analysis of explicit TSERKN methods for highly oscillatory systems

Numerical Algorithms
Symmetries of explicit Runge-Kutta methods

Numerical Algorithms
Trigonometrically fitted two-derivative Runge-Kutta methods for solving oscillatory differential equations

Numerical Algorithms

Quantified Score

Hi-index	0.24

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Quantified Score

Visualization

Abstract