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The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation

Akbar Mohebbi (University of Kashan, Kashan, Iran)
Mostafa Abbaszadeh (Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran)
Mehdi Dehghan (Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 28 October 2014

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Abstract

Purpose

The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation.

Design/methodology/approach

In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives.

Findings

The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy.

Originality/value

The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

Keywords

Citation

Mohebbi, A., Abbaszadeh, M. and Dehghan, M. (2014), "The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 8, pp. 1636-1659. https://doi.org/10.1108/HFF-08-2013-0254

Publisher

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Emerald Group Publishing Limited

Copyright © 2014, Emerald Group Publishing Limited