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.


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


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