عنوان مقاله [English]
In this paper, an efficient combination of the time-splitting and meshless local Petrov-Galerkin method for the numerical solution of Ginzburg–Landau equation in two and three dimensions is presented. The main idea of splitting scheme is separating the original equation in time into two parts, linear and nonlinear. Since, solving the nonlinear part based on the weak form is complicated and contains error, the split-step in time will be used. we solve the nonlinear part analytically and linear part numerically by the meshless local Petrov-Galerkin method in space variables and the Crank-Nicolson method in time. Hence, the moving Kriging interpolation is used instated of moving least squares. Therefore, the shape functions of the meshless local Petrov-Galerkin method have the Kronecker's delta property and the boundary conditions can be implemented directly and easily. Several examples for two and three dimensions are presented and the results are compared with their analytical solutions to demonstrate the validity and capability of this method.