IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v320y2018icp407-424.html
   My bibliography  Save this article

Application of wavelet collocation method for hyperbolic partial differential equations via matrices

Author

Listed:
  • Singh, Somveer
  • Patel, Vijay Kumar
  • Singh, Vineet Kumar

Abstract

In this work, we developed an efficient computational method based on Legendre and Chebyshev wavelets to find an approximate solution of one dimensional hyperbolic partial differential equations (HPDEs) with the given initial conditions. The operational matrices of integration for Legendre and Chebyshev wavelets are derived and utilized to transform the given PDE into the linear system of equations by combining collocation method. Convergence analysis and error estimation associated to the presented idea are also investigated under several mild conditions. Numerical experiments confirm that the proposed method has good accuracy and efficiency. Moreover, the use of Legendre and Chebyshev wavelets are found to be accurate, simple and fast.

Suggested Citation

  • Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:407-424
    DOI: 10.1016/j.amc.2017.09.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317306719
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.09.043?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. Razzaghi, M. & Yousefi, S., 2000. "Legendre wavelets direct method for variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(3), pages 185-192.
    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. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    4. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    5. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Haifa Bin Jebreen & Fairouz Tchier, 2020. "On the Numerical Simulation of HPDEs Using θ -Weighted Scheme and the Galerkin Method," Mathematics, MDPI, vol. 9(1), pages 1-13, December.

    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. S. Balaji, 2014. "Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-10, June.
    2. Yousefi, S. & Razzaghi, M., 2005. "Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 1-8.
    3. Gupta, Sandipan & Ranta, Shivani, 2022. "Legendre wavelet based numerical approach for solving a fractional eigenvalue problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Reza Doostaki & Mohammad Mehdi Hosseini, 2022. "Option Pricing by the Legendre Wavelets Method," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 749-773, February.

    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:320:y:2018:i:c:p:407-424. 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.