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Mathematical Problems in Engineering
Volume 2018, Article ID 2056834, 12 pages
https://doi.org/10.1155/2018/2056834
Research Article

Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions

1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor Darul Ehsan, Malaysia
2Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Gambang, Pahang, Malaysia
3Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor Darul Ehsan, Malaysia

Correspondence should be addressed to Zanariah Abdul Majid; moc.oohay@99dijam_anaz

Received 3 April 2018; Accepted 2 September 2018; Published 2 October 2018

Academic Editor: Nunzio Salerno

Copyright © 2018 Nadirah Mohd Nasir et al. 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

This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs) with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-corrector mode via shooting technique. The shooting method was adapted with the Newton divided difference interpolation approach as the strategy of seeking for the new initial estimate. Five numerical examples are included to examine and illustrate the practical usefulness of the proposed method. Numerical tested problem is also highlighted on the diffusion of heat generated application that imposed the Robin boundary conditions. The present findings revealed that the proposed method gives an efficient performance in terms of accuracy, total function calls, and execution time as compared with the existing method.