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Volume 17, Issue 2
Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations

Guang-Hua Gao & Hai-Wei Sun

DOI: 10.4208/cicp.180314.010914a

Commun. Comput. Phys., 17 (2015), pp. 487-509.

Published online: 2018-04

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  • Abstract

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.

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@Article{CiCP-17-487, author = {Guang-Hua Gao and Hai-Wei Sun}, title = {Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {2}, pages = {487--509}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180314.010914a}, url = {http://global-sci.org/intro/article_detail/cicp/10966.html} }
TY - JOUR T1 - Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations AU - Guang-Hua Gao & Hai-Wei Sun JO - Communications in Computational Physics VL - 2 SP - 487 EP - 509 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.180314.010914a UR - https://global-sci.org/intro/article_detail/cicp/10966.html KW - AB -

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.

Guang-Hua Gao and Hai-Wei Sun. (2018). Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations. Communications in Computational Physics. 17 (2). 487-509. doi:10.4208/cicp.180314.010914a
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