Stability of the analytic and numerical solutions for impulsive differential equations (Q643352)

The authors study the stability and the asymptotic stability of solution of the impulsive differential equation \[ \dot x(x)= f(x,t), \quad t>0,\;t\neq \tau _{k};\qquad \Delta x= I_{k}(x), \quad t=\tau_{k},\;x(0^{+})=x_{0} \] in assumption that this problem has a unique solution. A numerical solution of this problem is obtained for the particular case \( f(x,t)=d(x)x(t)\) using the parameter \(\theta\) for discrete equation. The stability of analytical and numerical solutions is established with the several supplementary conditions.