Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/205391 |
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| _version_ | 1832563140509827072 |
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| author | Omar Abu Arqub Zaer Abo-Hammour Shaher Momani Nabil Shawagfeh |
| author_facet | Omar Abu Arqub Zaer Abo-Hammour Shaher Momani Nabil Shawagfeh |
| author_sort | Omar Abu Arqub |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3904ef7b800648da93b799b3ec2c3566 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3904ef7b800648da93b799b3ec2c35662025-02-03T01:20:53ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/205391205391Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic AlgorithmOmar Abu Arqub0Zaer Abo-Hammour1Shaher Momani2Nabil Shawagfeh3Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanDepartment of Mechatronics Engineering, Faculty of Engineering, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanIn 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.http://dx.doi.org/10.1155/2012/205391 |
| spellingShingle | Omar Abu Arqub Zaer Abo-Hammour Shaher Momani Nabil Shawagfeh Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm Abstract and Applied Analysis |
| title | Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm |
| title_full | Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm |
| title_fullStr | Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm |
| title_full_unstemmed | Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm |
| title_short | Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm |
| title_sort | solving singular two point boundary value problems using continuous genetic algorithm |
| url | http://dx.doi.org/10.1155/2012/205391 |
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