A modified Runge-Kutta method for increasing stability properties

被引：4

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

共 50 条

[11] STRONG STABILITY OF EXPLICIT RUNGE-KUTTA TIME DISCRETIZATIONS
Sun, Zheng
Sho, Chi-Wang
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (03) : 1158 - 1182
[12] From semidiscrete to fully discrete: Stability of Runge-Kutta schemes by the energy method
Levy, D
Tadmor, E
SIAM REVIEW, 1998, 40 (01) : 40 - 73
[13] Paper A - and I -stability of Runge-Kutta collocation methods
Dujardin, Guillaume
Lacroix-Violet, Ingrid
APPLIED NUMERICAL MATHEMATICS, 2024, 202 : 158 - 172
[14] STABILITY PROBLEM CORRESPONDING TO RUNGE-KUTTA METHODS.
Scherer, R.
1600, (67):
[15] A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation
Simos, TE
Vigo-Aguiar, J
JOURNAL OF MATHEMATICAL CHEMISTRY, 2001, 30 (01) : 121 - 131
[16] The Runge-Kutta theory in a nutshell
Albrecht, P
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (05) : 1712 - 1735
[17] Runge-Kutta research at Toronto
Hull, TE
Enright, WH
Jackson, KR
APPLIED NUMERICAL MATHEMATICS, 1996, 22 (1-3) : 225 - 236
[18] Optimal implicit strong stability preserving Runge-Kutta methods
Ketcheson, David I.
Macdonald, Colin B.
Gottlieb, Sigal
APPLIED NUMERICAL MATHEMATICS, 2009, 59 (02) : 373 - 392
[19] The　Stability　of　Runge－Kutta　Methods　for　Systems　of　Delay　Differential　Equations
王晓彪
刘明珠
Journal of Harbin Institute of Technology(New series), 1996, (01) : 1 - 6
[20] Asymptotical stability of Runge-Kutta for a class of impulsive differential equations
Zhang, Gui-Lai
ADVANCES IN DIFFERENCE EQUATIONS, 2016, : 1 - 14

← 1 2 3 4 5 →