Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Article Title: Investigating Optimal Accuracy of a New Class of First Derivative Linear Multistep Method with Increasing Step - Size
by Famurewa O. K. E., and Olorunsola S. A.

Abstract:
In this study, the development of a new class of first derivative linear multistep method was examined for step - size (k) ranging from 1 - 4. The method is of the form; ' , with local truncation error; 'The study investigated the accuracy of the newly generated schemes which are variants of the 'first derivative linear multistep method', in order to determine the step - size with optimal accuracy. The development of the new schemes adopted Taylor Series expansion of functions and and involved the determination of the values of the unknown parameters and having imposed accuracy of order P on the local truncation error ( ) of the method. The results showed that the order of accuracy of the method increased from k=1 to k=2 and started decreasing from k=2 to k=4 with optimum accuracy obtained at k =2.

Keywords: multi-step, derivative, optimal, accuracy, step - size, local truncation error.

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