## Numerical methods for impulsive differential equation.(English)Zbl 1145.65317

Summary: In this paper, the asymptotical stability of the numerical methods with the constant stepsize for impulsive differential equation \begin{aligned} \dot x(t) & =\alpha x, \qquad t\neq k,t >0\\ \Delta x & = \sigma x,\qquad t=k\\ x(0 & +0)=x_0,\end{aligned} where $$a\neq 0, \beta, x_0 \in \mathbb R, 1 + \beta \neq 0, k\in \mathbb N$$, 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:

 65L05 Numerical methods for initial value problems involving ordinary differential equations

RODAS
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### References:

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