Existence, uniqueness and approximation of the solution of an ode with (infinitely many) state-dependent impulses via fixed mesh galerkin formulation

Abstract

A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (infinitely many) state-dependent impulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution. The convergence of the approximation is proved and its asymptotic order obtained.