Eur. Phys. J. Plus (2015) 130: 33
https://doi.org/10.1140/epjp/i2015-15033-5

Regular Article

Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation

¹ State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, 210098, Nanjing, China
² Department of Mathematics, Imam Khomeini International University, 34149-16818, Qazvin, Iran

^* e-mail: shivanian@sci.ikiu.ac.ir

Received: 10 October 2014
Revised: 29 December 2014
Accepted: 13 January 2015
Published online: 25 February 2015

Abstract

In this article, a general type of two-dimensional time-fractional telegraph equation explained by the Caputo derivative sense for (1 < α ≤ 2) is considered and analyzed by a method based on the Galerkin weak form and local radial point interpolant (LRPI) approximation subject to given appropriate initial and Dirichlet boundary conditions. In the proposed method, so-called meshless local radial point interpolation (MLRPI) method, a 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. The point interpolation method is proposed to construct shape functions using the radial basis functions. In the MLRPI 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. Two numerical examples are presented and satisfactory agreements are achieved.