Numerical Integration of Stiff System of Ordinary Differential Equations with a New K-step Rational Runge-Kutta Method

Abstract

The goal of this work is to develop, analyse and implement a K-step Implicit Rational Runge-Kutta schemes for Integration of Stiff system of Ordinary differential Equations. Its development adopted Taylor and Binomial series expansion Techniques to generate its parameters. The analysis of its basic properties adopted Dahlquist, A-stability model test equation and the results show that the scheme is Consistent, Convergent and A-stable. Numerical results show that the method is accurate and effective

Keywords: Rational, Runge-Kutta, Convergent, Consistent , Effective, Error bound, Implementation, Development, A-stable.