Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients |
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| Authors: | Mohammad Mahdi Izadkhah Jafar Saberi‐Nadjafi |
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| Affiliation: | Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran |
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| Abstract: | In this paper, we study the numerical solution to time‐fractional partial differential equations with variable coefficients that involve temporal Caputo derivative. A spectral method based on Gegenbauer polynomials is taken for approximating the solution of the given time‐fractional partial differential equation in time and a collocation method in space. The suggested method reduces this type of equation to the solution of a linear algebraic system. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | spectral methods Gegenbauer polynomials Caputo derivative time‐fractional diffusion equations |
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