EXPINT---A MATLAB package for exponential integrators

Authors:
Håvard Berland;Bård Skaflestad;Will M. Wright
Affiliations:
Norwegian University of Science and Technology, Trondheim, Norway;Norwegian University of Science and Technology, Trondheim, Norway;Norwegian University of Science and Technology, Trondheim, Norway
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2007

Citing 17
Cited 13

B-convergence results for linearly implicit one step methods

BIT
A method for exponential propagation of large systems of stiff nonlinear differential equations

Journal of Scientific Computing
Efficient solution of parabolic equations by Krylov approximation methods

SIAM Journal on Scientific and Statistical Computing
On Krylov Subspace Approximations to the Matrix Exponential Operator

SIAM Journal on Numerical Analysis
Exponential Integrators for Large Systems of Differential Equations

SIAM Journal on Scientific Computing
A new class of time discretization schemes for the solution of nonlinear PDEs

Journal of Computational Physics
High order Runge-Kutta methods on manifolds

proceedings of the on Numerical analysis of hamiltonian differential equations
Numerical methods for ordinary differential equations in the 20th century

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms
Exponential time differencing for stiff systems

Journal of Computational Physics
Commutator-free Lie group methods

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Computing a matrix function for exponential integrators

Journal of Computational and Applied Mathematics
Fourth-Order Time-Stepping for Stiff PDEs

SIAM Journal on Scientific Computing
Generalized integrating factor methods for stiff PDEs

Journal of Computational Physics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems

SIAM Journal on Numerical Analysis
B-series and Order Conditions for Exponential Integrators

SIAM Journal on Numerical Analysis
The scaling and modified squaring method for matrix functions related to the exponential

Applied Numerical Mathematics

Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation

Journal of Computational Physics
A rational Krylov method for solving time-periodic differential equations

Applied Numerical Mathematics
Comparison of methods for evaluating functions of a matrix exponential

Applied Numerical Mathematics
Implementation of exponential Rosenbrock-type integrators

Applied Numerical Mathematics
The scaling and modified squaring method for matrix functions related to the exponential

Applied Numerical Mathematics
Algorithm 894: On a block Schur--Parlett algorithm for ϕ-functions based on the sep-inverse estimate

ACM Transactions on Mathematical Software (TOMS)
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media

Journal of Computational Physics
On accurate product integration rules for linear fractional differential equations

Journal of Computational and Applied Mathematics
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
Exponential peer methods

Applied Numerical Mathematics
A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: Application to wood drying

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

Quantified Score

Hi-index	0.02

Visualization

Abstract

Recently, a great deal of attention has been focused on the construction of exponential integrators for semilinear problems. In this article we describe a MATLAB1 package which aims to facilitate the quick deployment and testing of exponential integrators, of Runge--Kutta, multistep, and general linear type. A large number of integrators are included in this package along with several well-known examples. The so-called ϕ functions and their evaluation is crucial for accuracy, stability, and efficiency of exponential integrators, and the approach taken here is through a modification of the scaling and squaring technique, the most common approach used for computing the matrix exponential.