Higher order Runge–Kutta methods for impulsive differential systems

This paper studies higher order approximations of solutions of differential equations with non-fixed times of impulses. We assume that the right-hand side is sufficiently smooth. Using a Runge–Kutta method of higher order and natural assumptions on the impulsive surfaces and the impulses, we calculate good approximations of the jump times, which enables us to extend the classical results for higher order of convergence of Runge–Kutta methods to more complicated systems.