Close Search Advanced
Journals
Resources
About Us
Open Access
Journals
Resources
About Us
Open Access

Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations

Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations
Preview
Add to basket

Year:    2015

Communications in Computational Physics, Vol. 17 (2015), Iss. 2 : pp. 487–509

Abstract

This paper is devoted to the discussion of numerical methods for solving two-dimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analyzed and the unconditional stabilities of the obtained schemes are investigated by Fourier analysis method. Numerical experiments show the effectiveness and the spatial higher-order accuracy of the proposed methods.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.180314.010914a

Communications in Computational Physics, Vol. 17 (2015), Iss. 2 : pp. 487–509

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:   

  1. Fourth-Order Numerical Solutions for a Fuzzy Time-Fractional Convection–Diffusion Equation under Caputo Generalized Hukuhara Derivative

    Zureigat, Hamzeh | Al-Smadi, Mohammed | Al-Khateeb, Areen | Al-Omari, Shrideh | Alhazmi, Sharifah E.

    Fractal and Fractional, Vol. 7 (2022), Iss. 1 P.47

    https://doi.org/10.3390/fractalfract7010047 [Citations: 13]

  2. On high-order compact schemes for the multidimensional time-fractional Schrödinger equation

    Eskar, Rena | Feng, Xinlong | Kasim, Ehmet

    Advances in Difference Equations, Vol. 2020 (2020), Iss. 1

    https://doi.org/10.1186/s13662-020-02946-w [Citations: 2]
  3. Numerical Methods for Fractional Differentiation

    Application to Ordinary Fractional Differential Equations

    Owolabi, Kolade M. | Atangana, Abdon

    2019

    https://doi.org/10.1007/978-981-15-0098-5_7 [Citations: 0]

  4. Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives

    Liu, Jian-Guo | Ma, Zheng | Zhou, Zhennan

    Journal of Scientific Computing, Vol. 72 (2017), Iss. 1 P.291

    https://doi.org/10.1007/s10915-017-0356-4 [Citations: 9]

  5. A Semidiscrete Finite Element Approximation of a Time-Fractional Fokker--Planck Equation with NonSmooth Initial Data

    Le, Kim Ngan | McLean, William | Mustapha, Kassem

    SIAM Journal on Scientific Computing, Vol. 40 (2018), Iss. 6 P.A3831

    https://doi.org/10.1137/17M1125261 [Citations: 12]

  6. Efficient compact finite difference method for variable coefficient fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions in conservative form

    Ren, Lei | Liu, Lei

    Computational and Applied Mathematics, Vol. 37 (2018), Iss. 5 P.6252

    https://doi.org/10.1007/s40314-018-0690-7 [Citations: 4]

  7. Alternating direction implicit finite difference method for time-fractional multi-asset Black-Scholes problem governing European options

    Gyulov, Tihomir B. | Koleva, Miglena N.

    EIGHTH INTERNATIONAL CONFERENCE NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES2021), (2022), P.030013

    https://doi.org/10.1063/5.0083615 [Citations: 0]

  8. An unconditionally stable linearized CCD–ADI method for generalized nonlinear Schrödinger equations with variable coefficients in two and three dimensions

    He, Dongdong | Pan, Kejia

    Computers & Mathematics with Applications, Vol. 73 (2017), Iss. 11 P.2360

    https://doi.org/10.1016/j.camwa.2017.04.009 [Citations: 25]

  9. Unique solvability of the CCD scheme for convection–diffusion equations with variable convection coefficients

    Wang, Qinghe | Pan, Kejia | Hu, Hongling

    Advances in Difference Equations, Vol. 2018 (2018), Iss. 1

    https://doi.org/10.1186/s13662-018-1591-1 [Citations: 3]

  10. A Fifth-Order Combined Compact Difference Scheme for Stokes Flow on Polar Geometries

    He, Dongdong | Pan, Kejia

    East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 P.714

    https://doi.org/10.4208/eajam.200816.300517a [Citations: 5]

  11. A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients

    Chen, Buyun | He, Dongdong | Pan, Kejia

    International Journal of Computer Mathematics, Vol. 96 (2019), Iss. 5 P.992

    https://doi.org/10.1080/00207160.2018.1478415 [Citations: 4]

  12. An efficient differential quadrature method for fractional advection–diffusion equation

    Zhu, X. G. | Nie, Y. F. | Zhang, W. W.

    Nonlinear Dynamics, Vol. 90 (2017), Iss. 3 P.1807

    https://doi.org/10.1007/s11071-017-3765-x [Citations: 19]

  13. Efficient compact finite difference methods for a class of time-fractional convection–reaction–diffusion equations with variable coefficients

    Wang, Yuan-Ming | Ren, Lei

    International Journal of Computer Mathematics, Vol. 96 (2019), Iss. 2 P.264

    https://doi.org/10.1080/00207160.2018.1437262 [Citations: 23]

  14. An unconditionally stable spatial sixth-order CCD-ADI method for the two-dimensional linear telegraph equation

    He, Dongdong

    Numerical Algorithms, Vol. 72 (2016), Iss. 4 P.1103

    https://doi.org/10.1007/s11075-015-0082-7 [Citations: 8]