Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

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

Document Type : Original Paper

Authors
Ali Shokri
Erfan Bahmani
Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran
10.22055/jamm.2020.27924.1668
Abstract
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.
Keywords
Direct meshless Local Petrov-Galerkin method
Moving least squares
Generalized moving least squares
Two-dimensional telegraph equation
The local weak form
Subjects
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Journal of Advanced Mathematical Modeling
Volume 10, Issue 2
December 2020
Pages 267-287

  • Receive Date 17 December 2018
  • Revise Date 13 March 2020
  • Accept Date 21 March 2020