An Improved Self-Starting Implicit Hybrid Method

Abstract

The paper presents the derivation a hybrid block method for the solutions of Initial Value Problems of Ordinary Differential Equations. This is achieved by using collocation and interpolation technique to contruct a self-starting method with continuous coefficients together with the additional methods from its first derivative which are combined to form a single block that simultaneously provide the approximate solutions for Initial Value Problem. The analysis of the properties of the method such as stability, consistency and convergence are discussed and the performance of the method is demonstrated on two test problems to show the accuracy and efficiency of the method. On comparison of the results obtained from numerical examples with some existing methods, we discovered that the method behaved favourably well.