Numerical Method Based on Galerkin Approximation for the Fractional Advection-Dispersion Equation

被引：0

作者：

Singh H. ^{[1
]}

Sahoo M.R. ^{[2
]}

Singh O.P. ^{[1
]}

机构：

[1] Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi

[2] School of Mathematical Sciences, National Institute of Science Education and Research (NISER), Khurda, 752050, Odisha

来源：

International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / 3期

关键词：

Convergence analysis; Fractional order advection-dispersion equation; Galerkin approximation; System of fractional order ODE;

D O I：

10.1007/s40819-016-0233-0

中图分类号：

学科分类号：

摘要：

In this paper, we present a numerical method for solving homogeneous as well as non-homogeneous fractional advection-dispersion equation (FADE). The numerical method is based on the Galerkin approximation. The Galerkin approximation converts the FADE into a system of fractional ordinary differential equations whose solutions is discussed. Convergence of the proposed method is shown. Numerical examples are given and numerical results are compared with exact solution to show the effectiveness and accuracy of the proposed method. © 2016, Springer India Pvt. Ltd.

引用

页码：2171 / 2187

页数：16

共 30 条

[1]

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

[2]

Bonilla B., Rivero M., Trujillo J.J., On system of linear fractional differential equations with constant coefficients, Appl. Math. Comput., 187, pp. 68-78, (2007)

[3]

Dehghan M., Numerical solution of three-dimensional advection-diffusion equation, Appl. Math. Comput., 150, pp. 5-19, (2004)

[4]

Dehghan M., Fully implicit finite difference methods for two-dimensional diffusion with non-local boundary condition, J. Comput. Appl. Math., 106, pp. 255-269, (1999)

[5]

Dehghan M., Fully explicit finite difference methods for two-dimensional diffusion with an integer condition, Nonlinear Anal. Theory Methods Appl., 48, pp. 637-650, (2002)

[6]

Diethelm K., Ford N.J., Freed A.D., Luchko Y., Algorithms for fractional calculus: a selection of numerical methods, Comput. Methods Appl. Mech. Eng., 194, pp. 743-773, (2005)

[7]

Gorenflo R., Mainardi F., Scalas E., Roberto M., Fractional calculus and continuous time finance, III. The diffusion limit, Math. Finance, Konstanz, 2000, pp. 171-180, (2001)

[8]

Hilfer R., Application of Fractional Calculus in Physics, (2000)

[9]

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

[10]

Joseph K.T., Sahoo M.R., Vanishing viscosity approach to a system of conservation laws admitting δ <sup>′ ′</sup> –waves. Commun. pure , Appl. Anal., 12, pp. 2091-2118, (2013)

← 1 2 3 →