A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations. (16th March 2016)

• Record Type: Journal Article
• Authors: Guo, Boling; Xu, Qiang; Zhu, Ailing
• Is Part Of: Communications in computational physics. Volume 19:Number 3(2016:Mar.)
• Page Start: 733
• Page End: 757
• Publication Date: 2016-03-16
• Subjects: 65M06, -- 26A33, -- 35R11; Fractional percolation equation, -- second-order finite difference method, -- Crank-Nicolson scheme, -- Richardson extrapolation, -- stability analysis; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.011214.140715a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.