IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v387y2020ics0096300319305478.html
   My bibliography  Save this article

A new high order ADI numerical difference formula for time-fractional convection-diffusion equation

Author

Listed:
  • Wu, Longyuan
  • Zhai, Shuying

Abstract

Based on exponential transformation, quadratic interpolation polynomial and Padé approximation, a new high order finite difference scheme is proposed for solving the two-dimensional (2D) time-fractional convection-dominated diffusion equation (of order α ∈ (0, 1)). The resulting scheme is of (3−α)-order accuracy in time and fourth-order accuracy in space. In order to reduce the amount of computation, the alternating direction implicit (ADI) scheme is further developed. Numerical experiments are given to demonstrate the high accuracy and robustness of our new scheme.

Suggested Citation

  • Wu, Longyuan & Zhai, Shuying, 2020. "A new high order ADI numerical difference formula for time-fractional convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    • Handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319305478
    DOI: 10.1016/j.amc.2019.124564
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319305478
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.124564?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Juan & Zhang, Xindong & Yang, Bohui, 2018. "An approximation scheme for the time fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 305-312.
    2. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    3. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    4. Meilan Qiu & Liquan Mei & Dewang Li, 2017. "Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-20, March.
    5. Behroozifar, M. & Sazmand, A., 2017. "An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 1-17.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jang, Bongsoo & Kim, Hyunju, 2024. "Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 60-79.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    2. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    3. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    4. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Jang, Bongsoo & Kim, Hyunju, 2024. "Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 60-79.
    6. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    8. Kumar, Devendra & Nama, Hunney & Baleanu, Dumitru, 2024. "Dynamical and computational analysis of fractional order mathematical model for oscillatory chemical reaction in closed vessels," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    9. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    10. Ahmed Gamal Atta & Waleed Mohamed Abd-Elhameed & Galal Mahrous Moatimid & Youssri Hassan Youssri, 2022. "A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    11. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.
    12. Singh, Anup & Das, Subir & Ong, S.H., 2022. "Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 491-500.
    13. Duan, Jun-Sheng & Qiu, Xiang, 2018. "Stokes’ second problem of viscoelastic fluids with constitutive equation of distributed-order derivative," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 130-139.
    14. Zhang, Yuxin & Li, Qian & Ding, Hengfei, 2018. "High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 432-443.
    15. Hashan, Mahamudul & Jahan, Labiba Nusrat & Tareq-Uz-Zaman, & Imtiaz, Syed & Hossain, M. Enamul, 2020. "Modelling of fluid flow through porous media using memory approach: A review," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 643-673.
    16. Faheem, Mo & Khan, Arshad & Raza, Akmal, 2022. "A high resolution Hermite wavelet technique for solving space–time-fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 588-609.
    17. Sweilam, Nasser Hassan & El-Sayed, Adel Abd Elaziz & Boulaaras, Salah, 2021. "Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Du, Rui & Sun, Dongke & Shi, Baochang & Chai, Zhenhua, 2019. "Lattice Boltzmann model for time sub-diffusion equation in Caputo sense," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 80-90.
    19. Singh, Harendra & Srivastava, H.M., 2019. "Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1130-1149.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319305478. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.