Indian Journal of Science and Technology

Abstract

Background/Objectives: Numerically solving second order Boundary Value Problems (BVPs) directly is an area that has drawn much attention in recent literature and hence the general aim of this article. Methods/Statistical Analysis: Block methods are developed using Taylor series approach and are applied to directly approximate the considered second order Boundary Value Problems. Certain specifications of the block method developed involves it being of step number k = 4 and order p = 5. This block method consists of mathematical expressions that will simultaneously provide results at the grid points and derivatives of the grid points for the k-step method. Findings: After the development of the new block method in this article, certain Boundary Value Problems are considered and the new block method is adopted to solve it numerically and comparison was made with their exact solution. The results show the new block method show superiority in comparison to other numerical methods of same order p = 5 adopted by other authors in previous literature. Hence, this new block method can be considered a more suitable numerical approach to approximate the numerical solutions of second order BVPs. Applications/Improvements: This block method is suitable for application in solving numerically second order BVPs with closer accuracy to the exact or analytic solutions of the differential equations under consideration. 
Keywords: Block Method, Boundary Value Problems, Four-Step, Order Five, Second Order