A Class of Implicit Five Step Hybrid Method for Solving First Order Initial Value Problem

Abstract

In this paper, a self-starting five step continuous block hybrid formulae (CBHF) with one Off-step point is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators that are of uniform order and are assembled in to a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the ordinary differential equations. The order of accuracy of the block method was discussed and its accuracy over the methods in literature is established numerically. The result of the proposed hybrid method performed absolutely better, when compared with the exact solution and the result obtained by Mohammed (2011), which are all of step five (i.e. k = 5).