On the preservation of invariants by explicit Runge-Kutta methods

被引：55
|
作者：
Calvo, M.
Hernandez-Abreu, D. [1 ]
Montijano, J. I.
Randez, L.
机构：
[1] Univ Zaragoza, Dept Matemat Aplicada, E-50009 Zaragoza, Spain
[2] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Spain
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2006年 / 28卷 / 03期
关键词：
initial value problems; explicit Runge-Kutta methods; numerical geometric integration; preservation of invariants; variable step-size codes;
D O I：
10.1137/04061979X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new strategy to preserve invariants in the numerical integration of initial value problems with explicit Runge-Kutta methods is presented. It is proved that this technique retains the order of the original method, has an easy and cheap implementation, and can be used in adaptive Runge-Kutta codes. Some numerical experiments with the classical code of Dormand and Prince, DoPri5(4), based on a pair of embedded methods with orders 5 and 4, are presented to show the behavior of the new method for several problems which possess invariants.
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页码：868 / 885
页数：18
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