A Class of Three Stage Implicit Rational Runge-Kutta Schemes for Approximation of Second Order Ordinary Differential Equations

Abstract

In this paper, 3 – stage Implicit Rational Runge – Kutta methods are derived using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. The efficiency of the method were tested on some numerical examples and found to give better approximations than the existing methods.

Keywords: Java Programming Language, Implicit Rational Runge Kutta scheme, Second order equations.