EXPODE -- 高级指数时间积分工具箱用于MATLAB
EXPODE -- Advanced Exponential Time Integration Toolbox for MATLAB
AI总结：
EXPODE工具箱提供五种指数积分器，用于求解（ mildly ）刚性常微分方程或时间依赖偏微分方程，通过矩阵函数与向量的稳定高效近似提升效率，支持直接对角化和Pade近似，并包含Krylov子空间方法。
摘要：
我们介绍了一个MATLAB工具箱，包含五种不同类别的指数积分器，用于求解（ mildly ）刚性常微分方程或时间依赖偏微分方程。为了提高此类指数积分器的效率，必须以稳定、可靠和高效的方式近似这些积分器中出现的矩阵函数与向量的乘积。该工具箱包含直接通过对角化或Pade近似计算矩阵函数的选项。对于大规模问题，还实现了Krylov子空间方法。该工具箱的主要动机是提供通用工具，一方面允许轻松运行不同指数积分器的实验，另一方面使其易于扩展，通过简单地包括其他方法或计算矩阵函数的其他选项来实现。因此，我们实现了该工具箱与MATLAB内置的ODE求解器兼容。大多数方法都可以使用自适应步长。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
