Genetic algorithms with Nelder-Mead optimization in the variational methods of boundary value problems

Authors:
Nikos E. Mastorakis
Affiliations:
WSEAS Research Dept, Agiou Ioannou Theologou, Zografou, Athens and Technical University of Sofia, English Language Faculty, Industrial Engineering Department and Military Institutes of University ...
Venue:
WSEAS Transactions on Mathematics
Year:
2009

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Abstract

The p-Laplacian equation is a generalization of the PDE of Laplace Equation and in this paper, we present a way of its solution using Finite Elements. Our method of Finite Elements leads to an Optimization Problem that can be solved by an appropriate combination of Genetic Algorithms and Nelder-Mead. Our method is illustrated by a numerical example. Other methods for the solution of other equations that contain the p-Laplacian operator are also discussed.