Development of a New Class of Block Implicit Runge-Kutta Type Method for Initial Value Problems

Abstract

In this study, we propose a new class of Runge-kutta type method with three stages for the solution of initial value problems. The method was developed through the collocation approach and reformulated into a Runge-kutta type of first order using the butcher analysis. The first order method was extended to a second order method using the Runge –kutta Nystrom method. A convergence Analysis was carried out in order to determine the order, error constant and stability analysis.Numerical examples carried out on the Initial value problems further substantiates the effectiveness and viability of the methods.