Derivation of an Implicit Runge – Kutta Method for First Order Initial Value Problem in Ordinary Differential Equation using Hermite, Laguerre and Legendre Polynomials.

Abstract

In this paper, three Implicit Runge – Kutta methods are derived using Hermite, Laguerre and Legendre polynomials for the direct solution of general first order initial value problems of ordinary differential equations with constant step size. The analysis of the properties of the developed methods were investigated and found to be consistent, convergent and A – stable. The efficiency of the methods were tested on some numerical examples and are found to give better approximations than the existing methods.

Keywords: Implicit Runge – Kutta shemes, Collocation, Interpolation, canonical polynomial and  A – stable.