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MLPG method for two-dimensional diffusion equation with Neumann’s and non-classical boundary conditions. (English) Zbl 1206.65229
Summary: A meshless local Petrov-Galerkin (MLPG) method is presented to treat parabolic partial differential equations with Neumann’s and non-classical boundary conditions. A difficulty in implementing the MLPG method is imposing boundary conditions. To overcome this difficulty, two new techniques are presented to use on square domains. These techniques are based on the finite differences and the moving least squares (MLS) approximations. The non-classical integral boundary condition is approximated using Simpson’s composite numerical integration rule and the MLS approximation. Two test problems are presented to verify the efficiency and accuracy of the method.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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