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

  • Vahid Reza Hosseini
  • Elyas ShivanianEmail author
  • Wen Chen
Regular Article

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.

Keywords

Root Mean Square Error Radial Basis Function Root Mean Square Meshless Method Thin Plate Spline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Vahid Reza Hosseini
    • 1
  • Elyas Shivanian
    • 2
    Email author
  • Wen Chen
    • 1
  1. 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and MaterialsHohai UniversityNanjingChina
  2. 2.Department of MathematicsImam Khomeini International UniversityQazvinIran

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