A New Class of A-stable Implicit Schemes for Treatment of Stiff System of Ordinary Differential Equations

Abstract

In this paper, a new class of A-Stable Implicit Rational Runge-Kutta schemes were developed, analyzed and computerized to solve stiff system of ordinary differential equations. The method is motivated by the Implicit Conventional Runge – Kutta Schemes and Rational function approximation.  While its development and analyses make use of Taylor series expansion (Taylor and Binomial) and Pade’s approximation techniques respectively.  The schemes are convergent and A-stable.

Keywords: Rational, Runge-Kutta, Consistent, effective, Error bound, Implementation, Convergent, A-stable, A (a) stable