A comparison of extended runge-kutta formulae based on variety of means to solve system of ivps

Abstract

Extended fourth order Runge-Kutta (RK) formulae based on Arithmetic Mean (AM), Geometric Mean (GM), Harmonic Mean (HaM), Heronian Mean (HeM), Root Mean Square (RM), Centroidal Mean (CeM) and Contraharmonic Mean (CoM) are developed to solve the system of linear differential equations.The accuracy of the new formulae are tested for five major Initial Value Problems (IVPs) from the real world applications.The algorithms governing the methods can easily be computerized.The investigation undertaken in this study reveals that the extended fourth order RK methods based on AM, and CeM suit well for the system of Initial Value Problems (IVPs).

Keywords:

• Runge-Kutta formula
• Arithmetic Mean
• Geometric Mean
• Harmonic Mean
• Heronian Mean
• Root Mean Square
• Centroidal Mean
• Contraharmonic Mean
• Ordinary differential equation and system of IVPs

C.R. Categories:

• G.1.7