A Class of Convergent Rational Runge-Kutta Schemes for solution Of Ordinary Differential Equations (ODEs)

Abstract

In this paper, a class of convergent implicit Rational Runge-Kutta schemes
using Taylor and binomial series expansion, are developed, analysed and
computerized to solve ODEs. Numerical results arising from the new schemes compare favourably with the existing Euler’s method. Furthermore, the results show that the schemes are effective and efficient.

Keywords: Implicit, Rational, Runge-Kutta, effective, efficient and convergent.