IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp532-557.html
   My bibliography  Save this article

L3 approximation of Caputo derivative and its application to time-fractional wave equation-(I)

Author

Listed:
  • Srivastava, Nikhil
  • Singh, Vineet Kumar

Abstract

In this manuscript, first of all, we have developed two novel numerical approximations (called L3 and ML3 approximation) of the Caputo fractional derivative of order α∈(1,2). We have used the cubic interpolating polynomial on uniform grid points [(tj−2,Uj−2), (tj−1,Uj−1), (tj,Uj), (tj+1,Uj+1)] for 2≤j≤k−1 while the quadratic interpolating polynomial is applied on the first interval [t0,t1]. We have modified the L3 approximation by using cubic Hermite interpolation in the sub-interval [t0,t2]. The novel L3 and ML3, both approximation are second order accurate for all α. Both approximations are tested on various examples and gives highly accurate results. Later, using this L3 approximation, a difference scheme is proposed to solve the time-fractional wave equation (TFWE). The proposed difference scheme is second order accurate in space and time for all α. The scheme is again tested on three numerical problems of TFWE, and the comparative study of the numerical results by the proposed scheme with some existing schemes is also provided to show the effectiveness and accuracy of our scheme.

Suggested Citation

  • Srivastava, Nikhil & Singh, Vineet Kumar, 2023. "L3 approximation of Caputo derivative and its application to time-fractional wave equation-(I)," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 532-557.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:532-557
    DOI: 10.1016/j.matcom.2022.10.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004049
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.10.003?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. Maurya, Rahul Kumar & Devi, Vinita & Srivastava, Nikhil & Singh, Vineet Kumar, 2020. "An efficient and stable Lagrangian matrix approach to Abel integral and integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    2. Alikhanov, Anatoly A. & Huang, Chengming, 2021. "A high-order L2 type difference scheme for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    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. Kedia, Nikki & Alikhanov, Anatoly A. & Singh, Vineet Kumar, 2024. "Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 337-354.
    2. Zhou, Ziyi & Zhang, Haixiang & Yang, Xuehua, 2024. "CN ADI fast algorithm on non-uniform meshes for the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamics," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    3. Xuhao Li & Patricia J. Y. Wong, 2022. "gL 1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.

    More about this item

    Keywords

    L3 approximation; ML3 approximation; Caputo derivative; Time-fractional wave equation; Finite difference scheme;
    All these keywords.

    JEL classification:

    • L3 - Industrial Organization - - Nonprofit Organizations and Public Enterprise

    Statistics

    Access and download statistics

    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:matcom:v:205:y:2023:i:c:p:532-557. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.