A Study on Convergence and Region of Absolute Stability of Implicit Two – Step Multiderivative Method for Solving Stiff Initial Value Problems of First Order Ordinary Differential Equations.

Abstract

This study investigated and related the convergence and region of absolute stability of an implicit two - step multiderivative method, used in solving sampled stiff initial value problem of first order ordinary differential equation. It adopted the general implicit multiderivative linear multistep method at step - number (k) = 2 with derivative order (l) varied from 1 - 6 to develop six different variants of the method. Boundary locus method was adopted to determine the intervals of absolute stability which were plotted on the complex plane to show the regions of absolute stability. The variant methods were used to solve sampled stiff initial value problem of first order ordinary differential equation. The resulting numerical solutions were compared with the exact solution to determine accuracy and convergence of the methods. The study showed that two - step first derivative, two - step second derivative, two - step third derivative, two - step fifth derivative method and two - step sixth derivative methods yielded more accurate and convergent results with wider regions of absolute stability than two - step fourth derivative.