Investigation of a one-step hybrid algorithm towards the solution of first order linear and nonlinear initial-value problems of ordinary differential equations (FOLNIVP)

Abstract

The aim of developing any numerical method is to complement the challenges inherent in obtaining the analytical solution of a differential equation, if at all a closed form solution does exist. In this study we present a one-step implicit code of order eight block algorithms for the purpose of utilizing data at points other than a whole step number. The major advantage of hybrid method is that they possess remarkably small error constants which translate to better approximation. These methods constitute a class of methods whose computational potentialities have probably not yet been fully exploited. Therefore, the performance of the derived block hybrid algorithm is investigated using some numerical examples for the purpose of demonstrating its validity and applicability. The results obtained revealed that the algorithm is suitable for solving first order linear and nonlinear initial value problems (IVPs) of ordinary differential equations.