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Abstract
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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.
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