Local integration of 2-D fractional telegraph equation via moving least squares approximation

• Published in: Engineering analysis with boundary elements Vol. 56; pp. 98 - 105
• Main Authors: Shivanian, Elyas, Abbasbandy, Saeid, Alhuthali, Mohammed S., Alsulami, Hamed H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2015
• Subjects: Approximation; Boundary conditions; Dirichlet problem; Finite element method; Fractional derivative; Fractional telegraph equation; Galerkin methods; Least squares method; Local weak formulation; Mathematical analysis; Meshless local Petrov–Galerkin (MLPG) method; Meshless methods; Moving least squares (MLS); Moving least squares (MLS); Local weak formulation; Fractional telegraph equation; Meshless local Petrov–Galerkin (MLPG) method; Fractional derivative
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2015.02.012

In this paper, a classical type of two-dimensional time-fractional telegraph equation defined by Caputo sense for (1<α<2) is analyzed by an approach based on the Galerkin weak form and moving least squares (MLS) approximation subject to given appropriate initial and Dirichlet boundary conditions. In the proposed method, which is a kind of the Meshless local Petrov–Galerkin (MLPG) method, meshless Galerkin weak form is applied to the interior nodes while the meshless collocation method is used for the nodes on the boundary, so the Dirichlet boundary condition is imposed directly. In MLPG method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares. The moving least squares approximation is proposed to construct shape functions. Two numerical examples are presented and satisfactory agreements are achieved.