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# Meshless Local Integral Equations Formulation for the 2D Convection-Diffusion Equations with a Nonlocal Boundary Condition

Department of Mathematics, Persian Gulf University, Bushehr, Iran, email: shirzadi@pgu.ac.ir, shirzadi.a@gmail.com

Computer Modeling in Engineering & Sciences 2012, 85(1), 45-64. https://doi.org/10.3970/cmes.2012.085.045

## Abstract

This paper presents a meshless method based on the meshless local integral equation (LIE) method for solving the two-dimensional diffusion and diffusion-convection equations subject to a non-local condition. Suitable finite difference scheme is used to eliminate the time dependence of the problem. A weak formulation on local subdomains with employing the fundamental solution of the Laplace equation as test function transforms the resultant elliptic type equations into local integral equations. Then, the Moving Least Squares (MLS) approximation is employed for discretizing spatial variables. Two illustrative examples with exact solutions being used as benchmark solutions are presented to show the efficiency of the proposed method.

## Keywords

APA Style
Shirzadi, A. (2012). Meshless local integral equations formulation for the 2D convection-diffusion equations with a nonlocal boundary condition. Computer Modeling in Engineering & Sciences, 85(1), 45-64. https://doi.org/10.3970/cmes.2012.085.045
Vancouver Style
Shirzadi A. Meshless local integral equations formulation for the 2D convection-diffusion equations with a nonlocal boundary condition. Comput Model Eng Sci. 2012;85(1):45-64 https://doi.org/10.3970/cmes.2012.085.045
IEEE Style
A. Shirzadi, "Meshless Local Integral Equations Formulation for the 2D Convection-Diffusion Equations with a Nonlocal Boundary Condition," Comput. Model. Eng. Sci., vol. 85, no. 1, pp. 45-64. 2012. https://doi.org/10.3970/cmes.2012.085.045

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