Multistep Block Method with Equidistant Hybrid Points for Solving Fifth Order Initial Value Problems

Ordinary differential equations (ODEs) that model real life scenarios as initial value problems (IVPs) mostly take the form of higher order IVPs. However, it is observed that numerical methods for the direct solution of fifth order IVPs are sparse in literature compared to methods for fourth order and lower. This can be as a result of the computational rigour attributed to its reduction to a system of first order IVPs or the difficulty in developing methods with better accuracy than existing studies. This article aims to develop a multistep hybrid block method which will be used as a direct solution of fifth order IVPs without reduction. Its implementation with hybrid points is to obtain better accuracy and this will be justified by comparing with existing studies. Hence, this article introduces a new accurate numerical method for the direct solution of fifth order IVPs.