On The Analysis of The Stability Functions Of Order Three And Four Numerical Integrator for Initial Value Problems

The Stability functions of numerical integrators for the solution of initial valueproblems (ivps) in Ordinary Differential Equations (ODEs) are of paramount interest as it helps to determine the suitability of the method for obtaining the solutions required. In this paper we analyze the stability functions of two new integrators of order three and four we derived. Our results shows that they are both A – stable and L – stable and hence can cope effectively with stiff problems.Keywords: Rational Integrator, Stability, Cartesian Coordinates, Initial Value Problems