IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/521342.html
   My bibliography  Save this article

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

Author

Listed:
  • Osvaldo Guimarães
  • José Roberto C. Piqueira
  • Marcio Lobo Netto

Abstract

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Suggested Citation

  • Osvaldo Guimarães & José Roberto C. Piqueira & Marcio Lobo Netto, 2011. "Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-20, July.
    • Handle: RePEc:hin:jnlmpe:521342
    DOI: 10.1155/2011/521342
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2011/521342.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2011/521342.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/521342?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guimarães, Osvaldo & Labecca, William & Piqueira, José R.C., 2021. "Tensor solutions in irregular domains: Eigenvalue problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 110-130.

    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:hin:jnlmpe:521342. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.