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Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations

Published online by Cambridge University Press:  22 January 2015

Guang-Hua Gao and
Hai-Wei Sun
Guang-Hua Gao
Affiliation:
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210046, P.R. China
Hai-Wei Sun*
Affiliation:
Department of Mathematics, University of Macau, Macao
*
*Email addresses: gaoguanghua1107@163.com (G. Gao), hsun@umac.mo (H. Sun)

Abstract

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This paper is devoted to the discussion of numerical methods for solving two-dimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analyzed and the unconditional stabilities of the obtained schemes are investigated by Fourier analysis method. Numerical experiments show the effectiveness and the spatial higher-order accuracy of the proposed methods.

Keywords

65M0665M1265N0665N12Time-fractional advection-diffusion equationscombined compact difference (CCD) schemeADIstabilityFourier analysis

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015, pp. 487 - 509
Copyright
Copyright © Global Science Press Limited 2015 

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