On a parallel mesh-chopping algorithm for a class of initial value problems using fourth-order explicit Runge-Kutta method

Abstract

In this paper, we extend the results of [Comput. Math. Appl. 35 (1998) 121] to the class of initial value problems y ̂ ′= f ̂ (x, y ̂ ) , y ̂ (x 0)= η ̂ 0 , represented as a system of first order differential equations. We propose a simple modification in the existing fourth-order Runge-Kutta method which makes it amenable to parallelization on p processors. A numerical example illustrating the theory is presented and theoretical estimates for speed up are given which are in agreement.