A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation

S. Abbasbandy, H. Roohani Ghehsareh, Ishak Hashim, A. Alsaedi

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

In this paper, a comparison between two common techniques based on the radial basis function (RBFs), direct and indirect approaches and their localized forms is performed to numerical investigation of the two-dimensional linear second-order hyperbolic telegraph equation. Four meshfree methods based on the strong form equation, the nonsymmetric radial basis function collocation method or Kansa's method, the method of approximate particular solutions and the localized versions of these methods are formulated and the performances of these methods for solving governing problem are compared. A time stepping approach is employed for the first and second order time derivatives. The multiquadrics (MQ) and inverse multiquadrics (IMQ) functions are used as basis functions for interpolating either unknown function or Laplacian of the unknown function in the proposed techniques. Some numerical results are given to demonstrate the validity and efficiency of these methods. Through the presented results, it can be observed that local versions of the methods have superior stability and efficiency and the global methods are sensitive to the shape parameter and large amount of collocation points.

Original languageEnglish
Pages (from-to)10-20
Number of pages11
JournalEngineering Analysis with Boundary Elements
Volume47
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Telegraph Equation
Telegraph
Meshfree
Hyperbolic Equations
Basis Functions
Radial Functions
Unknown
Meshfree Method
Particular Solution
Shape Parameter
Time Stepping
Linear Order
Collocation Method
Collocation
Numerical Investigation
Derivatives
First-order
Derivative
Numerical Results

Keywords

  • Global Kansa's method
  • Local radial basis function collocation methods
  • Meshfree method
  • Multiquadric radial basis functions
  • The method of approximate particular solutions
  • Two-dimensional linear hyperbolic equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Engineering(all)

Cite this

A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation. / Abbasbandy, S.; Roohani Ghehsareh, H.; Hashim, Ishak; Alsaedi, A.

In: Engineering Analysis with Boundary Elements, Vol. 47, No. 1, 2014, p. 10-20.

Research output: Contribution to journalArticle

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