SIAM Journal on Numerical Analysis
Some practical experience with the time integration of dissipative equations
Journal of Computational Physics
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
A fast spectral algorithm for nonlinear wave equations with linear dispersion
Journal of Computational Physics
SIAM Journal on Scientific Computing
Spectral methods in MatLab
Upwind scheme for non-hyperbolic systems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
The arbitrary order implicit multistep schemes of exponential fitting and their applications
Journal of Computational and Applied Mathematics
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Local discontinuous Galerkin methods for nonlinear Schrödinger equations
Journal of Computational Physics
High-order predictor-corrector of exponential fitting for the N-body problems
Journal of Computational Physics
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Journal of Computational Physics
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Exponential Runge-Kutta methods for parabolic problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Journal of Computational Physics
Applied Numerical Mathematics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
Journal of Computational Physics
Journal of Computational Physics
The LEM exponential integrator for advection-diffusion-reaction equations
Journal of Computational and Applied Mathematics
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
Letter to the Editor: Computing multiple integrals involving matrix exponentials
Journal of Computational and Applied Mathematics
A rational Krylov method for solving time-periodic differential equations
Applied Numerical Mathematics
Journal of Computational Physics
Compact integration factor methods in high spatial dimensions
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Exponential operator splitting time integration for spectral methods
Journal of Computational and Applied Mathematics
Smoothing schemes for reaction-diffusion systems with nonsmooth data
Journal of Computational and Applied Mathematics
Approximation of matrix operators applied to multiple vectors
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
Numerical Experiments for Reaction-Diffusion Equations Using Exponential Integrators
Numerical Analysis and Its Applications
A numerical simulation for the blow-up of semi-linear diffusion equations
International Journal of Computer Mathematics
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A small dispersion limit to the Camassa-Holm equation: A numerical study
Mathematics and Computers in Simulation
Exponential Runge--Kutta methods for parabolic problems
Applied Numerical Mathematics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
L2-stability analysis of novel ETD scheme for Kuramoto-Sivashinsky equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
On a prey-predator reaction-diffusion system with Holling type III functional response
Journal of Computational and Applied Mathematics
An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
Computers & Mathematics with Applications
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems
Journal of Computational Physics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
Generalized exponential time differencing methods for fractional order problems
Computers & Mathematics with Applications
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
A random map implementation of implicit filters
Journal of Computational Physics
Comparing leja and krylov approximations of large scale matrix exponentials
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Integrating factor methods as exponential integrators
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
A robust and efficient method for steady state patterns in reaction-diffusion systems
Journal of Computational Physics
Comparison of recurrence quantification methods for the analysis of temporal and spatial chaos
Mathematical and Computer Modelling: An International Journal
Fourth Order Time-Stepping for Kadomtsev-Petviashvili and Davey-Stewartson Equations
SIAM Journal on Scientific Computing
High-order symmetric multistep cosine methods
Applied Numerical Mathematics
Numerical investigations on the compressibility of a DPD fluid
Journal of Computational Physics
Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU
Journal of Computational Physics
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.56 |
We develop a class of numerical methods for stiff systems, based on the method of exponential time differencing. We describe schemes with second- and higher-order accuracy, introduce new Runge-Kutta versions of these schemes, and extend the method to show how it may be applied to systems whose linear part is nondiagonal. We test the method against other common schemes, including integrating factor and linearly implicit methods, and show how it is more accurate in a number of applications. We apply the method to both dissipative mad dispersive partial differential equations, after illustrating its behavior using forced ordinary differential equations with stiff linear parts.