A new fourth order runge-kutta formula based on the harmonic mean

Abstract

The new Runge-Kutta formulation using some other means other than the conventional arithmetic mean has resulted in the introduction of a number of new formulae for the numerical solution of ODE's. This paper discusses the derivation of a fourth order Runge-Kutta method based on the harmonic mean (HM) averaging of the functional values. The accuracy of the new formula is numerically examined.

Keywords:

• ODE solver
• Runge-Kutta
• arithmetic mean
• harmonic mean

C.R Categories:

• G1.7

^∗Universiti Teknologi Malaysia.

^∗Universiti Teknologi Malaysia.

Notes

^∗Universiti Teknologi Malaysia.