Projection methods preserving Lyapunov functions

被引：23

作者：

Calvo, M. ^{[2
]}

Laburta, M. P. ^{[1
]}

Montijano, J. I. ^{[2
]}

Randez, L. ^{[2
]}

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, IUMA, Ctr Politecn Super, Zaragoza 50018, Spain

[2] Univ Zaragoza, Fac Ciencias, Dept Matemat Aplicada, IUMA, E-50009 Zaragoza, Spain

来源：

BIT NUMERICAL MATHEMATICS | 2010年 / 50卷 / 02期

关键词：

Initial value problems; Lyapunov function; Numerical geometric integration; Projection methods; Explicit Runge-Kutta methods; RUNGE-KUTTA METHODS; FORMULAS;

D O I：

10.1007/s10543-010-0259-3

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we consider ordinary differential equations with a known Lyapunov function. We study the use of Runge-Kutta methods provided with a dense output and a projection technique to preserve any given Lyapunov function. This approach extends previous work of Grimm and Quispel (BIT 45, 2005), allowing the use of Runge-Kutta methods for which the associated quadrature formula does not need to have positive or zero coefficients. Some numerical experiments show the good performance of the proposed technique.

引用

页码：223 / 241

页数：19

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