EXPODE -- Advanced Exponential Time Integration Toolbox for MATLAB

TL;DR

EXPODE is a MATLAB toolbox offering multiple classes of exponential integrators for solving stiff differential equations, featuring various methods for computing matrix functions efficiently and designed for easy experimentation and extension.

Contribution

It introduces a flexible, extensible MATLAB toolbox for exponential integrators, supporting multiple methods and matrix function computations, tailored for stiff differential equations.

Findings

Supports five classes of exponential integrators.

Includes multiple matrix function approximation methods.

Designed for ease of use and extensibility in MATLAB.

Abstract

We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential integrators it is essential to approximate the products of the matrix functions arising in these integrators with vectors in a stable, reliable and efficient way. The toolbox contains options for computing the matrix functions directly by diagonalization or by Pade approximation. For large scale problems, Krylov subspace methods are implemented as well. The main motivation for this toolbox was to provide general tools which on one hand allows one to easily run experiments with different exponential integrators and on the other hand to make it easily extensible by making it simple to include other methods or other options to compute the matrix functions. Thus we implemented the toolbox to be compatible with the ode solvers included in MATLAB. Most of the methods can be used with adaptive stepping.