IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v74y2007i2p113-125.html
   My bibliography  Save this article

A numerical study of the long wave–short wave interaction equations

Author

Listed:
  • Borluk, H.
  • Muslu, G.M.
  • Erbay, H.A.

Abstract

Two numerical methods are presented for the periodic initial-value problem of the long wave–short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, second- and fourth-order versions of the split-step method, which are first-, second- and fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered.

Suggested Citation

  • Borluk, H. & Muslu, G.M. & Erbay, H.A., 2007. "A numerical study of the long wave–short wave interaction equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 113-125.
    • Handle: RePEc:eee:matcom:v:74:y:2007:i:2:p:113-125
    DOI: 10.1016/j.matcom.2006.10.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475406002540
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2006.10.016?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. Muslu, G.M. & Erbay, H.A., 2005. "Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(6), pages 581-595.
    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. Raviola, Lisandro A. & De Leo, Mariano F., 2024. "Performance of affine-splitting pseudo-spectral methods for fractional complex Ginzburg-Landau equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Ismail, M.S., 2008. "Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 532-547.
    3. Hederi, M. & Islas, A.L. & Reger, K. & Schober, C.M., 2016. "Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 101-113.

    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:74:y:2007:i:2:p:113-125. 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.