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

Boling Guo, Qiang Xu & Ailing Zhu

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://dor.org/10.4208/cicp.011214.140715a UR - https://global-sci.org/intro/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 & Ailing Zhu. (1970). 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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