Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations-Reference-Cited by-同舟云学术

Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Published:2020-01-21 Issue:1 Volume:2020 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Zhang Gui-Lai^ORCID

Abstract

AbstractIn this paper, asymptotical stability of the exact solutions of nonlinear impulsive ordinary differential equations is studied under Lipschitz conditions. Under these conditions, asymptotical stability of Runge–Kutta methods is studied by the theory of Padé approximation. And two simple examples are given to illustrate the conclusions.

Funder

Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-019-2473-x.pdf

Reference29 articles.

1. Bainov, D.D., Simeonov, P.S.: Systems with Impulsive Effect: Stability, Theory and Applications. Ellis Horwood, Chichester (1989)

2. Bainov, D.D., Simeonov, P.S.: Impulsive Differential Equations: Asymptotic Properties of the Solutions. World Scientific, Singapore (1995)

3. Butcher, J.C.: The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods. Wiley, New York (1987)

4. Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester (2003)

5. Dekker, K., Verwer, J.G.: Stability of Runge–Kutta Methods for Stiff Nonlinear Differential Equations. North-Holland, Amsterdam (1984)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Convergence, consistency and zero stability of impulsive one-step numerical methods;Applied Mathematics and Computation;2022-06

2. On numerical approximation of a delay differential equation with impulsive self-support condition;Applied Mathematics and Computation;2022-04

3. Stability Analysis of Multistage One-Step Multiderivative Methods for Nonlinear Impulsive Differential Equations in Banach Spaces;Mathematical Problems in Engineering;2021-12-17