IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4008-d956593.html
   My bibliography  Save this article

A Meshfree Approach for Solving Fractional Galilei Invariant Advection–Diffusion Equation through Weighted–Shifted Grünwald Operator

Author

Listed:
  • Farzaneh Safari

    (School of Mathematics and Statistics, Changsha University of Science and Technology, No. 960, 2nd Section, South Wanjiali Road, Tianxin District, Changsha 410004, China
    These authors contributed equally to this work.)

  • Qingshan Tong

    (School of Mathematics and Statistics, Changsha University of Science and Technology, No. 960, 2nd Section, South Wanjiali Road, Tianxin District, Changsha 410004, China
    These authors contributed equally to this work.)

  • Zhen Tang

    (School of Mathematics and Statistics, Changsha University of Science and Technology, No. 960, 2nd Section, South Wanjiali Road, Tianxin District, Changsha 410004, China)

  • Jun Lu

    (Nanjing Hydraulic Research Institute, Hujuguan 34 Road, Nanjing 210024, China)

Abstract

Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more general version that is the GIADE equation with nonlinear source term, is discretized by coupling weighted and shifted Grünwald difference approximation formulae and Crank–Nicolson technique. The new version of the backward substitution method, a well-established class of meshfree methods, is proposed for a numerical approximation of the consequent equation. In the present approach, the final approximation is given by the summation of the radial basis functions, the primary approximation, and the related correcting functions. Then, the approximation is substituted back to the governing equations where the unknown parameters can be determined. The polynomials, trigonometric functions, multiquadric, or the Gaussian radial basis functions are used in the approximation of the GIADE. Moreover, a quasilinearization technique is employed to transform a nonlinear source term into a linear source term. Finally, three numerical experiments in one and two dimensions are presented to support the method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4008-:d:956593
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4008/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4008/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Ndivhuwo Ndou & Phumlani Dlamini & Byron Alexander Jacobs, 2022. "Enhanced Unconditionally Positive Finite Difference Method for Advection–Diffusion–Reaction Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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).
    3. Heng Cheng & Zebin Xing & Yan Liu, 2023. "The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    4. 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).
    5. 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.
    6. Issa Omle & Ali Habeeb Askar & Endre Kovács & Betti Bolló, 2023. "Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges," Energies, MDPI, vol. 16(12), pages 1-27, June.
    7. Mahmoud Saleh & Endre Kovács & Imre Ferenc Barna & László Mátyás, 2022. "New Analytical Results and Comparison of 14 Numerical Schemes for the Diffusion Equation with Space-Dependent Diffusion Coefficient," Mathematics, MDPI, vol. 10(15), pages 1-26, August.
    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. Deka, Dharmaraj & Sen, Shuvam, 2022. "Compact higher order discretization of 3D generalized convection diffusion equation with variable coefficients in nonuniform grids," Applied Mathematics and Computation, Elsevier, vol. 413(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:gam:jmathe:v:10:y:2022:i:21:p:4008-:d:956593. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.