Optimization Solution of Troesch's and Bratu's Problems of Ordinary Type Using Novel Continuous Genetic Algorithm

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...

Full description

Saved in:
Bibliographic Details
Published inDiscrete Dynamics in Nature and Society Vol. 2014; no. 2014; pp. 52 - 66-105
Main Authors Abo-Hammour, Zaer, Abu Arqub, Omar, Momani, Shaher M., Shawagfeh, Nabil
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Subjects
Algorithms
Applied mathematics
Approximation
Boundary conditions
Colleges & universities
Derivatives
Differential equations
Digital computers
Dynamics
Functions, Continuous
Genetic algorithms
Mathematical analysis
Mathematical models
Mathematical research
Mathematics
Methods
Numerical analysis
Optimization
Optimization techniques
Ordinary differential equations
Science
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:1026-0226
1607-887X
DOI:10.1155/2014/401696