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Volume 19, Issue 3
A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations

Boling Guo, Qiang Xu & Ailing Zhu

DOI: 10.4208/cicp.011214.140715a

Commun. Comput. Phys., 19 (2016), pp. 733-757.

Published online: 2018-04

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  • Abstract

A finite difference method which is second-order accurate in time and in space is proposed for two-dimensional fractional percolation equations. Using the Fourier transform, a general approximation for the mixed fractional derivatives is analyzed. An approach based on the classical Crank-Nicolson scheme combined with the Richardson extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Consistency, stability and convergence of the method are established. Numerical experiments illustrating the effectiveness of the theoretical analysis are provided.

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@Article{CiCP-19-733, author = {Boling Guo, Qiang Xu and Ailing Zhu}, title = {A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {3}, pages = {733--757}, abstract = {

A finite difference method which is second-order accurate in time and in space is proposed for two-dimensional fractional percolation equations. Using the Fourier transform, a general approximation for the mixed fractional derivatives is analyzed. An approach based on the classical Crank-Nicolson scheme combined with the Richardson extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Consistency, stability and convergence of the method are established. Numerical experiments illustrating the effectiveness of the theoretical analysis are provided.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.011214.140715a}, url = {http://global-sci.org/intro/article_detail/cicp/11107.html} }
TY - JOUR T1 - A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations AU - Boling Guo, Qiang Xu & Ailing Zhu JO - Communications in Computational Physics VL - 3 SP - 733 EP - 757 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.011214.140715a UR - https://global-sci.org/intro/article_detail/cicp/11107.html KW - AB -

A finite difference method which is second-order accurate in time and in space is proposed for two-dimensional fractional percolation equations. Using the Fourier transform, a general approximation for the mixed fractional derivatives is analyzed. An approach based on the classical Crank-Nicolson scheme combined with the Richardson extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Consistency, stability and convergence of the method are established. Numerical experiments illustrating the effectiveness of the theoretical analysis are provided.

Boling Guo, Qiang Xu and Ailing Zhu. (2018). A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations. Communications in Computational Physics. 19 (3). 733-757. doi:10.4208/cicp.011214.140715a
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