Abstract
In the current work, a new aspect of the weak form meshless local Petrov-Galerkin method (MLPG), which is based on the particular solution is presented and well-used to numerical investigation of the two-dimensional diffusion equation with non-classical boundary condition. Two-dimensional diffusion equation with non-classical boundary condition is a challenged and complicated model in science and engineering. Also the method of approximate particular solutions (MAPS), which is based on the strong formulation is employed and performed to deal with the given non-classical problem. In both techniques an efficient technique based on the Tikhonov regularization technique with GCV function method is employed to solve the resulting ill-conditioned linear system. The obtained numerical results are presented and compared together through the tables and figures to demonstrate the validity and efficiency of the presented methods. Moreover the accuracy of the results is compared with the results reported in the literature. (C) 2013 Elsevier Ltd. All rights reserved.