Explicit Magnus expansions for nonlinear equations

被引:48
作者
Casas, Fernando [1 ]
Iserles, Arieh
机构
[1] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain
[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2006年 / 39卷 / 19期
关键词
D O I
10.1088/0305-4470/39/19/S07
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we develop and analyse new explicit Magnus expansions for the nonlinear equation Y' = A (t, Y) Y defined in a matrix Lie group. In particular, integration methods up to order four are presented in terms of integrals which can be either evaluated exactly or replaced by conveniently adapted quadrature rules. The structure of the algorithm allows us to change the step size and even the order during the integration process, thus improving its efficiency. Several examples are considered, including isospectral flows and highly oscillatory nonlinear differential equations.
引用
收藏
页码:5445 / 5461
页数:17
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