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INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 6, Issue 3, July 2017

Pages: 55-66

Date of Publication: 01-Jul-2017


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SIMULTANEOUS INCREASE IN STEP - NUMBER AND DERIVATIVE ORDER AND ITS EFFECT ON ACCURACY OF MULTIDERIVATIVE MULTISTEP METHOD.

Author: Famurewa O. K. E

Category: Engineering, Science and Mathematics

Abstract:

This paper discusses the effect of simultaneously increase in step - number (k) and order of derivative (l) on the accuracy of an implicit multiderivative method. The study varied k and l simultaneously from 1- 4 to produce some variants of the method. These variants were implemented by using them to solve two initial value problems of first order ordinary differential equations. A comparative study of the computed results was carried out which showed an improvement in accuracy as  k and l increased from k=1; l =1 to k=2; l =2 but accuracy reduced from k=3; l =3 to k=4; l =4, suggesting that two step second derivative scheme (k=2; l=2) has optimal accuracy when k and l were increased simultaneously.

Keywords: Step - number; Implicit; First Derivative; Accuracy; Ordinary Differential equation.