Numerical methods for impulsive differential equation

Authors:
X. J. Ran;M. Z. Liu;Q. Y. Zhu
Affiliations:
Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, 518055, PR China;Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, 518055, PR China;Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, 518055, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

Citing 3
Cited 1

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Global stability of sets for systems with impulses

Applied Mathematics and Computation
Stability of θ-methods for advanced differential equations with piecewise continuous arguments

Computers & Mathematics with Applications

Stability of the analytic and numerical solutions for impulsive differential equations

Applied Numerical Mathematics

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Abstract

In this paper, the asymptotical stability of the numerical methods with the constant stepsize for impulsive differential equation x@?(t)=@ax,tk,t0,@?x=@bx,t=k,x(0+0)=x"0, where @a0,@b,x"0@?R,1+@b0,k@?N, are investigated. The asymptotical stability conditions of the analytic solution of this equation and the numerical solutions are obtained. Finally, some experiments are given.