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Comparative Study of a New Scheme and Some Existing Methods for the Solution of Initial Value Problems in Ordinary Differential Equations
Abstract
In this paper, a new scheme was developed for the numerical solution of initial value problems of first order ordinary differential equations. The comparative study of the new scheme and some existing methods namely implicit linear six-step method and the classical Runge Kutta method were considered. To illustrate the superiority of the developed scheme over the implicit linear six-step method and the Runge kutta method, first order ordinary differential equations arising from real life situations was solved using MATLAB codes. The numerical results showed that the new scheme is efficient, accurate and performs better than its other counterparts.
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