Famurewa, O.K.E. and Olorunsola, S.A. (2014). Investigating optimal accuracy of a new class of first derivative linear multistep method with increasing step - size. Journa of Engineering and Applied Sciences, 5(6): 439 - 441.
INTRODUCTION
Mathematical analysis of real life problems, be it economics, social or scientific has become successful and widely adopted, this has been enhanced by the development of various numerical methods that has been tested accurate and efficient (Lambert, 2000).
A class of Implicit Multiderivative Linear Multistep Method was developed by Famurewa (2011), the method was tested and found to have better accuracy and larger interval of absolute stability than the conventional Adams Moulton’s linear multistep method of order 4.
According to Famurewa et al.; (2011), it was discovered that when the derivative properties of the method was increased, its accuracy improved. It was
also found out by Famurewa and Olorunsola (2013), that there is a limit to increasing the derivative properties, in order to achieve optimum accuracy.
The idea of a multistep method is to use previously calculated values at a number of mesh points to aid computation. According to Kirchgraber, (1986), a method that uses the values of the dependent variable y(x) and its derivative f1 (x; y) at k different mesh points x n -1, x n- 2 , . . . , x n- k
is called a multistep or a k step method.
Going by the assertion that linear multistep methods have better accuracy than the one step methods by sacrificing the one–step nature of the algorithm while retaining linearity (Butcher, 2008), and that linear multistep methods are important alternative to Runge–Kutta one step methods for the numerical solution of ordinary differential equations (Hairer, 2004), this study intends to determine the trend of accuracy of the newly developed method as the step size increases.