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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 205391, 25 pages
http://dx.doi.org/10.1155/2012/205391
Research Article

Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2Department of Mechatronics Engineering, Faculty of Engineering, The University of Jordan, Amman 11942, Jordan
3Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

Received 3 July 2012; Accepted 11 September 2012

Academic Editor: Svatoslav Staněk

Copyright © 2012 Omar Abu Arqub 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

In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.