Some Explicit Almost Runge – Kutta Methods for Solving Initial Value Problems

Abstract

Two new Explicit Almost Runge-Kutta methods for numerical integration of initial value problems are derived, by a judicious choice of the free parameters obtained after applying the order and stability conditions associated with Runge-Kutta methods. These methods which have the same number of stages as the order are of orders 4 and 5 i.e s=p=4 and s=p=5, respectively. Their convergence is established and numerical experiments with sample problems are conducted, in order to confirm their efficiency and reliability.