ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation

被引：35

作者：

Chen S. ^{[3
]}

Liu F. ^{[1
,2
]}

机构：

[1] School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001

[2] Department of Mathematical Sciences, Xiamen University

[3] Department of Mathematics, Quanzhou Normal University

来源：

J. Appl. Math. Comp. | 2008年 / 1-2卷 / 295-311期

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

Alternating directions implicit-Euler method; Fractional advection-dispersion equation; Richardson extrapolation; Stability and convergence; Two-dimensional problem;

D O I：

10.1007/s12190-007-0013-4

中图分类号：

学科分类号：

摘要：

In this paper, a two-dimensional fractional advection-dispersion equation (2D-FADE) with variable coefficients on a finite domain is considered. We use a new technique of combination of the Alternating Directions Implicit-Euler method (ADI-Euler), the unshifted Grünwald formula for the advection term, the right-shifted Grünwald formula for the diffusion term, and a Richardson extrapolation to establish an unconditionally stable second order accurate difference method. Stability, consistency and convergence of the ADI-Euler method for 2D-FADE are examined. A numerical example with known exact solution is also presented, and the behavior of the error is analyzed to verify the order of convergence of the ADI-Euler method and the extrapolated ADI-Euler method. © 2007 KSCAM and Springer-Verlag.

引用

页码：295 / 311

页数：16

共 26 条

[1]

Anh V.V., Leonenko N.N., Spectral analysis of fractional kinetic equations with random data, J. Stat. Phys., 104, pp. 1349-1387, (2001)

[2]

Anh V.V., Leonenko N.N., Renormalization and homogenization of fractional diffusion equations with random data, Probab. Theory Relat. Fields, 124, pp. 381-408, (2002)

[3]

Baeumer B., Meerschaert M.M., Benson D.A., Wheatcraft S.W., Subordinated advection-dispersion equation for contaminant transport, Water Resour. Res., 37, pp. 1543-1550, (2001)

[4]

Benson D.A., Wheatcraft S.W., Meerschaert M.M., Application of a fractional advection-dispersion equation, Water Resour. Res., 36, pp. 1403-1412, (2000)

[5]

Cushman J.H., Ginn T.R., Fractional advection-dispersion equation: a classical mass balance with convolution-Fickian flux, Water Resour. Res., 36, pp. 3763-3766, (2000)

[6]

Ervin V.S., Roop J.P., Variational solution of fractional advection dispersion equations on bounded domains in R d, Numer. Methods PDE, 22, pp. 558-576, (2006)

[7]

Huang F., Liu F., The fundamental solution of the space-time fractional advection-dispersion equation, J. Appl. Math. Comput., 18, pp. 339-350, (2005)

[8]

Husain I., Jabeen Z., On fractional programming containing support, J. Appl. Math. Comput., 18, pp. 361-376, (2005)

[9]

Isaacson E., Keller H.B., Analysis of Numerical Methods, (1966)

[10]

Jumarie G., A nonrandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional moises (FLQG), J. Appl. Math. Comput., 19, pp. 19-32, (2005)

← 1 2 3 →