指数积分器
数学
雅可比矩阵与行列式
矩阵指数
Krylov子空间
特征向量
数学分析
指数函数
微分方程
应用数学
后向微分公式
常系数
刚性方程
线性系统
线性微分方程
数值积分
微分代数方程
常微分方程
物理
量子力学
作者
Marlis Hochbruck,Christian Lubich,Hubert Selhofer
标识
DOI:10.1137/s1064827595295337
摘要
We study the numerical integration of large stiff systems of differential equations by methods that use matrix--vector products with the exponential or a related function of the Jacobian. For large problems, these can be approximated by Krylov subspace methods, which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators. The exponential methods also offer favorable properties in the integration of differential equations whose Jacobian has large imaginary eigenvalues. We derive methods up to order 4 which are exact for linear constant-coefficient equations. The implementation of the methods is discussed. Numerical experiments with reaction-diffusion problems and a time-dependent Schrödinger equation are included.
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