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

In 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...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 12
Main Author: Zhang, Gui-Lai
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 21.01.2020
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Asymptotic methods
Asymptotic properties
Asymptotical stability
Difference and Functional Equations
Differential equations
Exact solutions
Functional Analysis
Impulsive differential equation
Lipschitz condition
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Ordinary Differential Equations
Pade approximation
Partial Differential Equations
Runge-Kutta method
Stability
Impulsive differential equation
Runge–Kutta method
Lipschitz condition
Asymptotical stability
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:In 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.
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2473-x