Step size bounds for a class of multiderivative explicit Runge-Kutta methods

Abstract

A class of 3-Stage Multiderivative Explicit Runge-Kutta Methods was developed for the solution of Initial Value Problems (IVPs) in Ordinary Differential Equations. In this work, we present the bounds on the step size required for the implementation of this family of methods. This bound is one of the parameter required in the design of program codes for solving IVPs. A comparison of the step size bound was made vis-a-vis the existing Explicit Runge-Kutta Methods using some standard problems. The computation shows that the family of methods competes well with the popular methods. © 2012 Springer-Verlag.