A modified Runge-Kutta method for increasing stability properties

被引：3

作者：

Hu, Guang-Da ^{[1
,2
]}

Wang, Zheng ^{[2
]}

机构：

[1] Shanghai Customs Coll, Shanghai 201204, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 441卷

基金：

中国国家自然科学基金;

关键词：

Control theory; Nonlinear ODEs; Runge-Kutta methods; Increasing stability properties; Gradient; NONLINEAR CONTROL;

D O I：

10.1016/j.cam.2023.115698

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In control theory, we are interested mainly in investigating asymptotic stability of systems. In this paper explicit Runge-Kutta methods are investigated for numerical solutions of nonlinear ODEs with known strict Lyapunov functions. In order to increase stability properties, a modified version of explicit Runge-Kutta methods is presented. The modified Runge-Kutta method is explicit. It is different from the projection methods in literature which are implicit. Comparing with the standard Runge-Kutta method, the modified Runge-Kutta one has better stability properties. Numerical examples are provided to illustrate the effectiveness of the modified Runge-Kutta method.

引用

页数：8

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