Solution of Laplace equation using continuous genetic algorithms

In this paper, a novel method based on continuous genetic algorithms (CGAs) for the solution of Laplace s 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.