A numerical method for solving the time variable fractional order mobile-immobile advection-dispersion model

被引：47

作者：

Jiang, Wei ^{[1
]}

Liu, Na ^{[1
]}

机构：

[1] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2017年 / 119卷

基金：

中国国家自然科学基金;

关键词：

Mobile-immobile; Advection-dispersion equation; Spline space; Fractional derivative; SOLUTE TRANSPORT; EQUATION; MEDIA;

D O I：

10.1016/j.apnum.2017.03.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile-immobile advection-dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection-dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order gamma (x, t) is an element of [0, 1]. In order to solve this kind of equation, we discuss and derive the epsilon-approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：18 / 32

页数：15

共 15 条

[1]

[Anonymous], 2010, FUNCTIONAL ANAL

[2] NUMERICAL SCHEMES WITH HIGH SPATIAL ACCURACY FOR A VARIABLE-ORDER ANOMALOUS SUBDIFFUSION EQUATION [J].

Chen, Chang-Ming ;

Liu, F. ;

Anh, V. ;

Turner, I. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (04) :1740-1760

[3] Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media [J].

Chen, S. ;

Liu, F. ;

Burrage, K. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 67 (09) :1673-1681

[4]

Chen Z, 2011, IAHS-AISH P, V341, P154

[5] Mechanics with variable-order differential operators [J].

Coimbra, CFM .

ANNALEN DER PHYSIK, 2003, 12 (11-12) :692-703

[6]

Cui M., 2009, NONLINEAR NUMERICAL

[7] Effective ADE models for first-order mobile-immobile solute transport: Limits on validity and modeling implications [J].

Hansen, Scott K. .

ADVANCES IN WATER RESOURCES, 2015, 86 :184-192

[8] Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation [J].

Liu, F. ;

Zhuang, P. ;

Anh, V. ;

Turner, I. ;

Burrage, K. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) :12-20

[9]

Liu F., 2003, Journal of Applied Mathematics and Informatics, V13, P233

[10]

Mainardi F., 2001, Fract. Calc. Appl. Anal, V4, P153, DOI DOI 10.1007/BF02935797

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