Journal
APPLIED NUMERICAL MATHEMATICS
Volume 61, Issue 2, Pages 170-180Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2010.09.002
Keywords
MLPG method; Neumann's boundary conditions; Non-classical integral boundary condition; Finite differences; Heat equation; Parabolic partial differential equations
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In this paper, 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. 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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
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