Work

Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses

Year: 2024

Type: article

Abstract: In this paper, we study the asymptotical stability of the exact solutions of nonlinear impulsive differential equations with the Lipschitz continuous function f(t,x) for the dynamic system and for the impulsive term Lipschitz continuous delayed functions Ik. In order to obtain numerical methods with a high order of convergence and that are capable of preserving the asymptotical stability of the exact solutions of these equations, impulsive discrete Runge–Kutta methods and impulsive continuous Runge–Kutta methods are constructed, respectively. For these different types of numerical methods, different convergence results are obtained and the sufficient conditions for asymptotical stability of these numerical methods are also obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results.

Source: Mathematics

DOI: 10.3390/math12193002

Authors: Gui-Lai Zhang, Zhi-Yong Zhu, Yu-Chen Wang, Chao Liu

Institution: Northeastern University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hebei Province