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International Journal of Differential Equations
Volume 2017 (2017), Article ID 2464759, 12 pages
https://doi.org/10.1155/2017/2464759
Research Article

A Family of Boundary Value Methods for Systems of Second-Order Boundary Value Problems

1Department of Mathematics and Computer Science, Sule Lamido University, PMB 048, Kafin Hausa, Nigeria
2Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA

Correspondence should be addressed to T. A. Biala

Received 10 July 2016; Accepted 13 November 2016; Published 15 January 2017

Academic Editor: Elena Braverman

Copyright © 2017 T. A. Biala and S. N. Jator. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A family of boundary value methods (BVMs) with continuous coefficients is derived and used to obtain methods which are applied via the block unification approach. The methods obtained from these continuous BVMs are weighted the same and are used to simultaneously generate approximations to the exact solution of systems of second-order boundary value problems (BVPs) on the entire interval of integration. The convergence of the methods is analyzed. Numerical experiments were performed to show efficiency and accuracy advantages.