Higher Order Runge-Kutta Methods for Impulsive Differential Systems

R. Baier, Q. Din, T. D. Donchev: Higher Order Runge-Kutta Methods for Impulsive Differential Systems
Applied Mathematics and Computation, 218, (24), 11790 - 11798, 2012

DOI: 10.1016/j.amc.2012.05.037
MR Nummer: 2945182
Zentralblattnummer: 06242369
Keywords: impulsive differential equations; Runge-Kutta methods; variable times of impulses
Mathematics Subject Classification Code: 34A37 (65L06 65L20 49M25 34A36)


Abstract:

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.

Contents:

1. Preliminaries
2. Runge-Kutta approximation of the solution
3. Numerical examples
4. Concluding remarks

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