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Mathematical Problems in Engineering
Volume 2014, Article ID 747490, 10 pages
http://dx.doi.org/10.1155/2014/747490
Research Article

Solving Partial Differential Equations Using a New Differential Evolution Algorithm

Sustainable Infrastructure Research and Development Center, Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon kaen 40002, Thailand

Received 7 February 2014; Accepted 26 May 2014; Published 12 June 2014

Academic Editor: Khai Ching Ng

Copyright © 2014 Natee Panagant and Sujin Bureerat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proposes an alternative meshless approach to solve partial differential equations (PDEs). With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA) is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE) is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.