IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p923-d273285.html
   My bibliography  Save this article

Approximate Solutions of Time Fractional Diffusion Wave Models

Author

Listed:
  • Abdul Ghafoor

    (Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KP, Pakistan)

  • Sirajul Haq

    (Faculty of Engineering Sciences, GIK Institute, Topi 23640, KP, Pakistan)

  • Manzoor Hussain

    (Faculty of Engineering Sciences, GIK Institute, Topi 23640, KP, Pakistan)

  • Poom Kumam

    (Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Muhammad Asif Jan

    (Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KP, Pakistan)

Abstract

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

Suggested Citation

  • Abdul Ghafoor & Sirajul Haq & Manzoor Hussain & Poom Kumam & Muhammad Asif Jan, 2019. "Approximate Solutions of Time Fractional Diffusion Wave Models," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:923-:d:273285
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/923/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/923/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arbabi, Somayeh & Nazari, Akbar & Darvishi, Mohammad Taghi, 2017. "A two-dimensional Haar wavelets method for solving systems of PDEs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 33-46.
    2. Haq, Sirajul & Ghafoor, Abdul & Hussain, Manzoor, 2019. "Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 107-121.
    3. Fengying Zhou & Xiaoyong Xu, 2017. "Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-17, September.
    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. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2022. "An Explicit Wavelet Method for Solution of Nonlinear Fractional Wave Equations," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    2. Lin Chen & Wenzhi Xu & Zhuojia Fu, 2022. "A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation," Mathematics, MDPI, vol. 10(6), pages 1-15, March.

    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. Wei, Leilei & Li, Wenbo, 2021. "Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 280-290.
    2. Wei, Leilei & Wang, Huanhuan, 2023. "Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 685-698.
    3. Haq, Sirajul & Ghafoor, Abdul & Hussain, Manzoor, 2019. "Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 107-121.
    4. Sadri, Khadijeh & Aminikhah, Hossein, 2021. "An efficient numerical method for solving a class of variable-order fractional mobile-immobile advection-dispersion equations and its convergence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(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:7:y:2019:i:10:p:923-:d:273285. 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.