The Stability of Order m = 4 Rational Integrator for the Solution of Ordinary Differential Equation

In this article, investigation is carried out on a rational interpolation scheme of order m = 4, through two major processes of converting the resulting rational function to a complex outlook, and then, transforming the complex function to a polar form, from which the stability region of the method is constructed in the form of Jordan Curve. The regions of stability and instability as well as the encroachment interval of the scheme is determined with the use of Maple-18 and Matlab packages.