Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm
-
- Zaer Abo-Hammour
- Department of Mechatronics Engineering, Faculty of Engineering, The University of Jordan, Amman 11942, Jordan
-
- Omar Abu Arqub
- Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, Salt 19117, Jordan
-
- Shaher Momani
- Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
-
- Nabil Shawagfeh
- Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, Salt 19117, Jordan
説明
<jats:p>A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch’s and Bratu’s problems. The underlying idea of the method is to convert the two differential problems into discrete versions by replacing each of the second derivatives by an appropriate difference quotient approximation. The new method has the following characteristics. First, it should not resort to more advanced mathematical tools; that is, the algorithm should be simple to understand and implement and should be thus easily accepted in the mathematical and physical application fields. Second, the algorithm is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical and physical problems. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. The algorithm is tested on different versions of Troesch’s and Bratu’s problems. Experimental results show that the proposed algorithm is effective, straightforward, and simple.</jats:p>
収録刊行物
-
- Discrete Dynamics in Nature and Society
-
Discrete Dynamics in Nature and Society 2014 1-15, 2014
Hindawi Limited
