EXISTENCE,UNIQUENESS AND APPROXIMATION OF THE SOLUTION OF AN ODE WITH (INFINITELY MANY) STATE-DEPENDENT IMPULSES VIA FIXED MESH GALERKIN FORMULATION

摘要

A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses 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 asymptatic order obtained.