IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v70y2005i1p1-8.html
   My bibliography  Save this article

Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations

Author

Listed:
  • Yousefi, S.
  • Razzaghi, M.

Abstract

A numerical method for solving the nonlinear Volterra–Fredholm integral equations is presented. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties together with the Gaussian integration method are then utilized to reduce the Volterra–Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:1:p:1-8
    DOI: 10.1016/j.matcom.2005.02.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847540500090X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2005.02.035?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. Amiri, Sadegh & Hajipour, Mojtaba & Baleanu, Dumitru, 2020. "A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    2. Mirzaee, Farshid & Hadadiyan, Elham, 2016. "Numerical solution of Volterra–Fredholm integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 110-123.
    3. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Chen, Zhong & Jiang, Wei, 2015. "An efficient algorithm for solving nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 614-619.
    5. Beiglo, H. & Gachpazan, M., 2020. "Numerical solution of nonlinear mixed Volterra-Fredholm integral equations in complex plane via PQWs," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    6. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.
    7. Balcı, Mehmet Ali & Sezer, Mehmet, 2016. "Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 33-41.
    8. Erfanian, Majid & Mansoori, Amin, 2019. "Solving the nonlinear integro-differential equation in complex plane with rationalized Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 223-237.
    9. Sahu, P.K. & Ray, S.Saha, 2015. "Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 715-723.
    10. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2016. "Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 637-644.

    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. 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.
    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:matcom:v:70:y:2005:i:1:p:1-8. 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.