S. Abbasbandy1,2, V. Sladek3, A. Shirzadi1, J. Sladek3
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 15-38, 2011, DOI: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… More >
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