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Numerical Simulations for Coupled Pair of Diffusion Equations by MLPG Method

S. Abbasbandy1,2, V. Sladek3, A. Shirzadi1, J. Sladek3
Department of Mathematics, Imam Khomeini International University, Ghazvin 34149, Iran
*Corresponding author, Tel.: +98-912-1305326; fax: +98-281-3780040; E-mail address: abbas-bandy@ikiu.ac.ir (S. Abbasbandy)
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia

Computer Modeling in Engineering & Sciences 2011, 71(1), 15-38. https://doi.org/10.3970/cmes.2011.071.015

Abstract

This paper deals with the development of a new method for solution of initial-boundary value problems governed by a couple of nonlinear diffusion equations occurring in the theory of self-organization in non-equilibrium systems. The time dependence is treated by linear interpolation using the finite difference method and the semi-discrete partial differential equations are considered in a weak sense by using the local integral equation method with approximating 2-d spatial variations of the field variables by the Moving Least Squares. The evaluation techniques are discussed and the applicability of the presented method is demonstrated on two illustrative examples with exact solutions being used as benchmark solutions.

Keywords

MLPG, Moving least squares approximation, Numerical integration procedures, System of parabolic partial differential equations, Boundary conditions.

Cite This Article

Abbasbandy, S., Sladek, V., Shirzadi, A., Sladek, J. (2011). Numerical Simulations for Coupled Pair of Diffusion Equations by MLPG Method. CMES-Computer Modeling in Engineering & Sciences, 71(1), 15–38.



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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