A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation

A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation

Year:    2017

Author:    Can Li, Weihua Deng

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 282–306

Abstract

The second order weighted and shifted Grünwald difference (WSGD) operators are developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order WSGD operators; by properly choosing the weighted parameters, they can be effectively used to discretize space (Riemann-Liouville) fractional derivatives. Based on the new second order WSGD operators, we derive a family of difference schemes for the space fractional advection diffusion equation. By von Neumann stability analysis, it is proved that the obtained schemes are unconditionally stable. Finally, extensive numerical experiments are performed to demonstrate the performance of the schemes and confirm the convergence orders.

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/aamm.2015.m1069

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 282–306

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Riemann-Liouville fractional derivative WSGD operator fractional advection diffusion equation finite difference approximation stability.

Author Details

Can Li

Weihua Deng

  1. R. Chan’s circulant-based approximate inverse preconditioning iterative method for solving second-order space fractional advection–dispersion equations with variable coefficients

    Tang, Shi-Ping | Yang, Ai-Li | Zhou, Jian-Lin | Wu, Yu-Jiang

    Computational and Applied Mathematics, Vol. 43 (2024), Iss. 2

    https://doi.org/10.1007/s40314-024-02592-y [Citations: 0]
  2. Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients

    Lin, Fu-Rong | She, Zi-Hang

    Applied Numerical Mathematics, Vol. 167 (2021), Iss. P.281

    https://doi.org/10.1016/j.apnum.2021.05.007 [Citations: 7]
  3. Fast algorithm based on the novel approximation formula for the Caputo-Fabrizio fractional derivative

    Liu, Yang | Fan, Enyu | Yin, Baoli | Li, Hong

    AIMS Mathematics, Vol. 5 (2020), Iss. 3 P.1729

    https://doi.org/10.3934/math.2020117 [Citations: 13]
  4. DNT preconditioner for one-sided space fractional diffusion equations

    Lin, Fu-Rong | Qu, Hai-Dong | She, Zi-Hang

    BIT Numerical Mathematics, Vol. 61 (2021), Iss. 4 P.1311

    https://doi.org/10.1007/s10543-021-00858-z [Citations: 1]
  5. On a second order scheme for space fractional diffusion equations with variable coefficients

    Vong, Seakweng | Lyu, Pin

    Applied Numerical Mathematics, Vol. 137 (2019), Iss. P.34

    https://doi.org/10.1016/j.apnum.2018.12.002 [Citations: 12]
  6. Efficient preconditioner of one-sided space fractional diffusion equation

    Lin, Xue-Lei | Ng, Michael K. | Sun, Hai-Wei

    BIT Numerical Mathematics, Vol. 58 (2018), Iss. 3 P.729

    https://doi.org/10.1007/s10543-018-0699-8 [Citations: 22]
  7. A Fast Preconditioned Semi-Implicit Difference Scheme for Strongly Nonlinear Space-Fractional Diffusion Equations

    Huang, Yu-Yun | Gu, Xian-Ming | Gong, Yi | Li, Hu | Zhao, Yong-Liang | Carpentieri, Bruno

    Fractal and Fractional, Vol. 5 (2021), Iss. 4 P.230

    https://doi.org/10.3390/fractalfract5040230 [Citations: 10]
  8. Necessity of introducing non-integer shifted parameters by constructing high accuracy finite difference algorithms for a two-sided space-fractional advection–diffusion model

    Yin, Baoli | Liu, Yang | Li, Hong

    Applied Mathematics Letters, Vol. 105 (2020), Iss. P.106347

    https://doi.org/10.1016/j.aml.2020.106347 [Citations: 20]
  9. Numerical algorithms for the time-space tempered fractional Fokker-Planck equation

    Sun, Xiaorui | Zhao, Fengqun | Chen, Shuiping

    Advances in Difference Equations, Vol. 2017 (2017), Iss. 1

    https://doi.org/10.1186/s13662-017-1317-9 [Citations: 5]
  10. Solving time fractional partial differential equations with variable coefficients using a spatio-temporal meshless method

    Qiu, Xiangyun | Yue, Xingxing

    AIMS Mathematics, Vol. 9 (2024), Iss. 10 P.27150

    https://doi.org/10.3934/math.20241320 [Citations: 0]
  11. A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

    Almoaeet, Mohammed K. | Shamsi, Mostafa | Khosravian‐Arab, Hassan | Torres, Delfim F. M.

    Mathematical Methods in the Applied Sciences, Vol. 42 (2019), Iss. 10 P.3465

    https://doi.org/10.1002/mma.5592 [Citations: 4]
  12. Banded Preconditioners for Riesz Space Fractional Diffusion Equations

    She, Zi-Hang | Lao, Cheng-Xue | Yang, Hong | Lin, Fu-Rong

    Journal of Scientific Computing, Vol. 86 (2021), Iss. 3

    https://doi.org/10.1007/s10915-020-01398-4 [Citations: 9]
  13. A non‐standard finite difference method for space fractional advection–diffusion equation

    Liu, Ziting | Wang, Qi

    Numerical Methods for Partial Differential Equations, Vol. 37 (2021), Iss. 3 P.2527

    https://doi.org/10.1002/num.22734 [Citations: 3]
  14. An explicit form for higher order approximations of fractional derivatives

    Gunarathna, W.A. | Nasir, H.M. | Daundasekera, W.B.

    Applied Numerical Mathematics, Vol. 143 (2019), Iss. P.51

    https://doi.org/10.1016/j.apnum.2019.03.017 [Citations: 8]
  15. An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays

    Kıvanç Kürkçü, Ömür | Aslan, Ersin | Sezer, Mehmet

    The European Physical Journal Plus, Vol. 134 (2019), Iss. 8

    https://doi.org/10.1140/epjp/i2019-12761-4 [Citations: 10]
  16. A Class of Unconditioned Stable 4-Point WSGD Schemes and Fast Iteration Methods for Space Fractional Diffusion Equations

    She, Zi-Hang

    Journal of Scientific Computing, Vol. 92 (2022), Iss. 1

    https://doi.org/10.1007/s10915-022-01860-5 [Citations: 5]