IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v348y2019icp57-69.html
   My bibliography  Save this article

Numerical simulation for the space-fractional diffusion equations

Author

Listed:
  • Kheybari, Samad
  • Darvishi, Mohammad Taghi
  • Hashemi, Mir Sajjad

Abstract

This paper presents, a novel semi-analytical algorithm, based on the Chebyshev collocation method, for the solution of space-fractional diffusion equations. The original fractional equation is transformed into a system of ordinary differential equations (ODEs) by the Chebyshev collocation method. A new semi-analytical method is then used to approximate the solution of the resulting system. To emphasize the reliability of the new scheme, a convergence analysis is presented. It is shown that highly accurate solutions can be achieved with relatively few approximating terms and absolute errors are rapidly decrease as the number of approximating terms is increased. By presenting some numerical examples, we show that the proposed method is a powerful and reliable algorithm for solving space-fractional diffusion equations and can be extended to solve another space-fractional partial differential equations. Comparison with other methods in the literature, demonstrates that the proposed method is both efficient and accurate.

Suggested Citation

  • Kheybari, Samad & Darvishi, Mohammad Taghi & Hashemi, Mir Sajjad, 2019. "Numerical simulation for the space-fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 57-69.
  • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:57-69
    DOI: 10.1016/j.amc.2018.11.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318310154
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.11.041?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. Sweilam, N.H. & Nagy, A.M. & El-Sayed, Adel A., 2015. "Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 141-147.
    2. Kheybari, S. & Darvishi, M.T., 2018. "An efficient technique to find semi-analytical solutions for higher order multi-point boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 76-93.
    3. Lin, Ji & Reutskiy, S.Y. & Lu, Jun, 2018. "A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 459-476.
    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. Kheybari, Samad, 2021. "Numerical algorithm to Caputo type time–space fractional partial differential equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 66-85.
    2. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. 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).
    4. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    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. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    2. Lin, Ji & Reutskiy, Sergiy, 2020. "A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. Nagy, A.M., 2017. "Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 139-148.
    4. Agarwal, P. & El-Sayed, A.A., 2018. "Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 40-49.
    5. Farzaneh Safari & Qingshan Tong & Zhen Tang & Jun Lu, 2022. "A Meshfree Approach for Solving Fractional Galilei Invariant Advection–Diffusion Equation through Weighted–Shifted Grünwald Operator," Mathematics, MDPI, vol. 10(21), pages 1-18, October.
    6. Kheybari, Samad, 2021. "Numerical algorithm to Caputo type time–space fractional partial differential equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 66-85.
    7. Fengxin Sun & Jufeng Wang & Xiang Kong & Rongjun Cheng, 2021. "A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems," Mathematics, MDPI, vol. 9(19), pages 1-15, October.
    8. Zhang, Yuhui & Rabczuk, Timon & Lin, Ji & Lu, Jun & Chen, C.S., 2024. "Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    9. Sweilam, Nasser H. & Abou Hasan, Muner M. & Baleanu, Dumitru, 2017. "New studies for general fractional financial models of awareness and trial advertising decisions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 772-784.
    10. Lin, Ji & Zhang, Yuhui & Reutskiy, Sergiy & Feng, Wenjie, 2021. "A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 398(C).

    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:348:y:2019:i:c:p:57-69. 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.