Volume :2 , Issue :4 ,Page :162-197

Abstract :The aim of this paper is focused on developi ng a new fifth order fifth-stage Runge-Kutta method based on Heronian Mean to compute numerical solutions of Initial Value Problems (IVPs) in ODEs. The stability polynomial and the stability re gion of the new formula are obtained. A modest effort has been taken to examine the suitability, ado ptability and accuracy of the method. Based on the numerical results, it is observed that the presently developed new method is superior compared to some existing methods including fifth order Runge-Kutta methods based on Harmonic Mean and Contra Harmonic Mean.