On the preservation of invariants by explicit Runge-Kutta methods

被引：59

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.

引用

页码：868 / 885

页数：18

共 15 条

[1]

[Anonymous], 1941, PRINCETON MATH SERIE

[2]

CALVO M, 2004, EXPLICIT RUNGE KUTTA

[3] An iterative approximation scheme for the Landau-Lifshitz-Gilbert equation [J].