The numerical computation of differential equations cannot be overemphasized as it is evident in the literatures. It has been observed that analytical solution of some differential equations are intractable, hence there is need to seek for an alternative solution to such equations. Circumventing this problem resulted into an approximate solution otherwise known as numerical solution. There are so many numerical methods that can be used in solving differential equations which include predictor – corrector method which is linear multistep in nature and not self-starting method. In this presentation the focus is on presenting a self-starting multistep method for direct solution of Second Order Ordinary Differential Equations as against the popular predictor – corrector method which needs additional value for starting point which may alter the accuracy of the method. The method is a mixture of grid and off grid collocation point and often refer to as Block linear multistep method.
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