Symplectic integrators for second-order linear non-autonomous equations

被引：6
|
作者：
Bader, Philipp [1 ]
Blanes, Sergio [2 ]
Casas, Fernando [3 ,4 ]
Kopylov, Nikita [2 ]
Ponsoda, Enrique [2 ]
机构：
[1] La Trobe Univ, Dept Math & Stat, Bundoora, Vic 3086, Australia
[2] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia, Spain
[3] Univ Jaume 1, IMAC, Castellon de La Plana 12071, Spain
[4] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 330卷
关键词：
Second-order linear differential equations; Non-autonomous; Symplectic integrators; Magnus expansion; Matrix Hill's equation; SPLITTING METHODS; ALGORITHMS; EFFICIENT;
D O I：
10.1016/j.cam.2017.03.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes. (C) 2017 Elsevier B.V. All rights reserved.
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页码：909 / 919
页数：11
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