IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-59384-5_27.html
   My bibliography  Save this book chapter

Spectral Lanczos’ Tau Method for Systems of Nonlinear Integro-Differential Equations

In: Integral Methods in Science and Engineering, Volume 1

Author

Listed:
  • P. B. Vasconcelos

    (University of Porto, Center of Mathematics
    University of Porto, Economics Faculty)

  • J. Matos

    (University of Porto, Center of Mathematics
    Polytechnic School of Engineering Porto)

  • M. S. Trindade

    (University of Porto, Center of Mathematics)

Abstract

In this paper an extension of the spectral Lanczos’ tau method to systems of nonlinear integro-differential equations is proposed. This extension includes (i) linearization coefficients of orthogonal polynomials products issued from nonlinear terms and (ii) recursive relations to implement matrix inversion whenever a polynomial change of basis is required and (iii) orthogonal polynomial evaluations directly on the orthogonal basis. All these improvements ensure numerical stability and accuracy in the approximate solution. Exposed in detail, this novel approach is able to significantly outperform numerical approximations with other methods as well as different tau implementations. Numerical results on a set of problems illustrate the impact of the mathematical techniques introduced.

Suggested Citation

  • P. B. Vasconcelos & J. Matos & M. S. Trindade, 2017. "Spectral Lanczos’ Tau Method for Systems of Nonlinear Integro-Differential Equations," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 0, pages 305-314, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59384-5_27
    DOI: 10.1007/978-3-319-59384-5_27
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    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:spr:sprchp:978-3-319-59384-5_27. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.