Abstract

This work describes the development, analysis, implementation and a comparative study of a class of Implicit Multi-derivative Linear Multistep methods for numerical solution of non-stiff and stiff Initial Value Problems of first order Ordinary Differential Equations. These multi-derivative methods incorporate more analytical properties of the differential equation into the conventional implicit linear multistep formulae and vary the step-size (k) as well as the order of the derivative (l) to obtain more accurate and efficient methods for solution of non-stiff and stiff first order ordinary differential equations. The basic properties of these methods were analyzed and the results showed that the methods are accurate, convergent and A-stable. Hence, suitable for the solution of non-stiff and stiff initial value problems of ordinary differential equations. A comparative study of the newly developed methods are carried out to determine the effect of increasing the step-size (k) and the order of the derivative (l). The result showed a remarkable improvement in accuracy and efficiency as the step-size (k) and the order of the derivative (l) are increased.

Key words: Implicit, Multi-derivative, Multi-step, Non-stiff, Stiff, Ordinary and Differential equation.