On the derivation and implementation of inverse four stage Runge-Kutta methods for solving Initial Value Problems (IVPS) in ordinary differential equations

Abstract

A four-stage inverse Runge-Kutta method for solving the numerical solution of initial value problems (IVPs) in ordinary differential equations (ODEs) is initiated. Numerical experiments were implemented with the aid of the computer application software Maple 18 to determine the level of performance, accuracy and consistency of the method. The resulting numerical evidences show that this method gives satisfactory results.

Keywords: Runge-Kutta methods, inverse methods, four-stage