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Zbl 1145.65317
Ran, X.J.; Liu, M.Z.; Zhu, Q.Y.
Numerical methods for impulsive differential equation. (English)
[J] Math. Comput. Modelling 48, No. 1-2, 46-55 (2008). ISSN 0895-7177

Summary: In this paper, the asymptotical stability of the numerical methods with the constant stepsize for impulsive differential equation $$\aligned \dot x(t) & =\alpha x, \qquad t\ne k,t >0\\ \Delta x & = \sigma x,\qquad t=k\\ x(0 & +0)=x_0,\endaligned$$ where $a\ne 0, \beta, x_0 \in \Bbb R, 1 + \beta \ne 0, k\in \Bbb N$, are investigated. The asymptotical stability conditions of the analytic solution of this equation and the numerical solutions are obtained. Finally, some experiments are given.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)

Keywords: impulsive differential equation; asymptotical stability; $\theta $-method; Runge-Kutta method

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