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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

x ˙(t)=αx,tk,t>0Δx=σx,t=kx(0+0)=x 0 ,

where a0,β,x 0 ,1+β0,k, 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:
65L05Initial value problems for ODE (numerical methods)
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