GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Using Krylov methods in the solution of large-scale differential-algebraic systems
SIAM Journal on Scientific Computing
Avoiding BDF stability barriers in the MOL solution of advection-dominated problems
Applied Numerical Mathematics - Special issue on numerical methods for ordinary differential equations
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
CVODE, a stiff/nonstiff ODE solver in C
Computers in Physics
Numerical methods and software for sensitivity analysis of differential-algebraic systems
Applied Numerical Mathematics
Efficient sensitivity analysis of large-scale differential-algebraic systems
Applied Numerical Mathematics
Consistent Initial Condition Calculation for Differential-Algebraic Systems
SIAM Journal on Scientific Computing
A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
ACM Transactions on Mathematical Software (TOMS)
Application of parallel implicit methods to edge-plasma numerical simulations
Journal of Computational Physics
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Analyzing radiation diffusion using time-dependent sensitivity-based techniques
Journal of Computational Physics
PVODE, an ODE Solver for Parallel Computers
International Journal of High Performance Computing Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Analyzing radiation diffusion using time-dependent sensitivity-based techniques
Journal of Computational Physics
Second-order accurate projective integrators for multiscale problems
Journal of Computational and Applied Mathematics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Declarative temporal data models for sensor-driven query processing
DMSN '07 Proceedings of the 4th workshop on Data management for sensor networks: in conjunction with 33rd International Conference on Very Large Data Bases
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
Finding alternatives and reduced formulations for process-based models
Evolutionary Computation
Bayesian System Identification of Molecular Cascades
Neural Information Processing
A parallel computational model for sensitivity analysis in optimization for robustness
Optimization Methods & Software
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Attention in Cognitive Systems
A Parallel Algorithm To Solve Large Stiff ODE Systems On Grid Systems
International Journal of High Performance Computing Applications
A global strategy for solving reactive transport equations
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Application of a control vector parameterization method using an interior point algorithm
MIC '08 Proceedings of the 27th IASTED International Conference on Modelling, Identification and Control
insilicoSim: an extendable engine for parallel heterogeneous biophysical simulations
Proceedings of the 3rd International ICST Conference on Simulation Tools and Techniques
Environmental Modelling & Software
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Divide and recycle: types and compilation for a hybrid synchronous language
Proceedings of the 2011 SIGPLAN/SIGBED conference on Languages, compilers and tools for embedded systems
Long-time integration methods for mesoscopic models of pattern-forming systems
Journal of Computational Physics
Design and development of software tools for Bio-PEPA
Winter Simulation Conference
Mixed-level embedding and JIT compilation for an iteratively staged DSL
WFLP'10 Proceedings of the 19th international conference on Functional and constraint logic programming
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Hypergraph partitioning for the parallel computation of continuous Petri nets
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
Estimating Computational Noise
SIAM Journal on Scientific Computing
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Applied Numerical Mathematics
Non-standard semantics of hybrid systems modelers
Journal of Computer and System Sciences
Estimating Derivatives of Noisy Simulations
ACM Transactions on Mathematical Software (TOMS)
From hybrid data-flow languages to hybrid automata: a complete translation
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Journal of Computational Neuroscience
SIAM Journal on Scientific Computing
Snoopy --- a unifying petri net tool
PETRI NETS'12 Proceedings of the 33rd international conference on Application and Theory of Petri Nets
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
ACM Transactions on Mathematical Software (TOMS)
Parallel computation of continuous Petri nets based on hypergraph partitioning
The Journal of Supercomputing
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
Bounds on the reachable sets of nonlinear control systems
Automatica (Journal of IFAC)
Zélus: a synchronous language with ODEs
Proceedings of the 16th international conference on Hybrid systems: computation and control
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
Computers & Mathematics with Applications
Hypergraph partitioning for the parallel computing of fuzzy differential equations
Fuzzy Sets and Systems
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Proceedings of the International Conference on Computer-Aided Design
Computers in Biology and Medicine
Lyapunov exponents computation for hybrid neurons
Journal of Computational Neuroscience
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
Journal of Computational Physics
Petri Net-Based Collaborative Simulation and Steering of Biochemical Reaction Networks
Fundamenta Informaticae - Dedicated to the Memory of Professor Manfred Kudlek
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SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.