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Volume :37 Issue : 2 2010      Add To Cart                                                                    Download

Solution of Laplace equation using continuous genetic algorithms

Auther : ZAER S. ABO-HAMMOUR*, RAMZI B. ALBADARNEH** AND

  • Department of Mechatronics Engineering, University of Jordan.

    E-mail: zaer_hr@yahoo.com.

    Department of Basic Science and Math., Philadelphia University.

    E-mail: rbalbdarnt06@sci.ju.edu.jo.

    Department of Computer Engineering, Mutah University.

    E-mail: m_srayeh@mutah.edu.jo.

    ABSTRACT

  1.  

    In this paper, a novel method based on continuous genetic algorithms (CGAs) for the solution of Laplaces equations in two-dimensional rectangular regions has been developed. The algorithm converts the given differential equation into an algebraic equation in the first phase. After that, the overall residual error is calculated for all unknown nodes based on the values generated by the CGAs. The problem is then converted into a minimization problem of the overall residue of all nodes. The proposed method handles problems of the Dirichlet and Neumann type, and is considered an extension of the single dimensional case of CGAs previously developed by the principal author.

     

    Keywords: Continuous Genetic Algorithms; Laplace Equation; Numerical Solution, Partial Differential Equations.

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