Numerical solution of the 2D telegraph equation using direct meshless local Petrov-Galerkin (DMLPG) method

The two most important numerical methods, finite difference, and finite element methods have some limitations in solving some problems arising in partial differential equations. A meshless method can be used to overcome these limitations. In these methods, no mesh required in the domain to solve the problem, and just scattered points are used for the approximation of the unknown function. In this paper, the two-dimensional telegraph equation is solved using a direct meshless local Petrov-Galerkin (DMLPG) method based on generalized moving least squares. To measure the accuracy of this method, the comparison of the results with the theoretical solution and other methods has been used, which results indicate the high accuracy of the proposed method.