Direct Solution of Initial Value Problems of Fourth Order Ordinary Differential Equations Using Modified Implicit Hybrid Block Method

Our focus in this article is the derivation; analysis and implementation of a new modified implicit hybrid block method for the direct solution of initial value problems of fourth order ordinary differential equations. In the derivation of the method, we adopted the approach of collocation approximation to obtain the main scheme with continuous coefficients. From the main scheme, additional schemes were developed. The implementation strategy of the new method is by combining the main scheme and the additional schemes as simultaneous integrator to initial value problem of fourth order ordinary differential equations. As required of any numerical method, the properties analysis of the block was done and the result showed that it is consistent, convergent, zero stable and absolutely stable. We then test our method with numerical examples solved using existing method and were found to give better results.