Approximation of state-dependent impulsive ordinary differential equations
In this work we consider approximations to the solution of a system of ordinary differential equations (ODE) in presence of possibly infinitely many state dependent impulses on the righthand side. We use a simple transformation that allows us to show that the problem is equivalent to an ordinary differential equation without impulse with its solution in H-1(0, T; E). This transformation is numerically important. Indeed, to approximate the solution of the initial problem, we just have to approximate the solution of the equivalent problem which is regular. We then obtain better rates of convergence. Moreover we obtain an approximation of the solution which looks like the initial solution. Both, the solution and its approximation, are in BV(0, T; E), the space of functions of bounded variation on [0, T].
impulse ordinary differential equation galerkin method numerical scheme