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A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation

Ali Shokri1, Mehdi Dehghan1
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran.
E-mail addresses: shokri.a@gmail.com (A. Shokri), mdehghan@aut.ac.ir; mdehghan.aut@gmail.com (M. Dehghan).

Computer Modeling in Engineering & Sciences 2012, 84(4), 333-358. https://doi.org/10.3970/cmes.2012.084.333

Abstract

The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method.

Keywords

Two-dimensional complex Ginzburg-Landau (GL) equation, Periodic boundary conditions, Radial Basis Functions (RBFs), Multiquadrics (MQ), Thin Plate Splines (TPS), Collocation, Predictor-corrector.

Cite This Article

Shokri, A., Dehghan, M. (2012). A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation. CMES-Computer Modeling in Engineering & Sciences, 84(4), 333–358.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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