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A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations

Part of: Miscellaneous topics - Partial differential equations Partial differential equations, initial value and time-dependent initial-boundary value problems Real functions

Published online by Cambridge University Press:  16 March 2016

Boling Guo ,
Qiang Xu  and
Ailing Zhu
Boling Guo
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Qiang Xu*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
Ailing Zhu
Affiliation:
School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
*
* Corresponding author. Email addresses:gbl@iapcm.ac.cn (B. Guo), xuqiangsdu@gmail.com (Q. Xu), zhuailing88@126.com (A. Zhu)
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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.

Keywords

Fractional percolation equationsecond-order finite difference methodCrank-Nicolson schemeRichardson extrapolationstability analysis

MSC classification

Secondary: 65M06: Finite difference methods 26A33: Fractional derivatives and integrals 35R11: Fractional partial differential equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 733 - 757
Copyright
Copyright © Global-Science Press 2016 

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