A New 4 th Order Hybrid Runge-Kutta Methods for Solving Initial Value Problems (IVPs)

Recently, there has been a great deal of interest in the formulation of Runge-Kutta methods based on averages other than the conventional Arithmetic Mean for the numerical solution of Ordinary differential equations. In this paper, a new 4th Order Hybrid Runge-Kutta method based on linear combination of Arithmetic mean, Geometric mean and the Harmonic mean to solve first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented. Also the stability region for the method is shown. Moreover, the new method is compared with Runge-Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results indicate that the performance of the new method show superiority in terms of accuracy to some of other well known methods in literature and the stability investigation is in agreement with the known fourth order Runge-Kutta methods but with excellent stability region.