IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v199y2022icp394-413.html
   My bibliography  Save this article

A locally stabilized radial basis function partition of unity technique for the sine–Gordon system in nonlinear optics

Author

Listed:
  • Nikan, O.
  • Avazzadeh, Z.

Abstract

This paper develops a localized radial basis function partition of unity method (RBF-PUM) based on a stable algorithm for finding the solution of the sine–Gordon system. This system is one useful description for the propagation of the femtosecond laser optical pulse in a systems of two-level atoms. The proposed strategy approximates the unknown solution through two main steps. First, the time discretization of the problem is accomplished by a difference formulation with second-order accuracy. Second, the space discretization is obtained using the local RBF-PUM. This method authorizes us to tackle the high computational time related to global collocation techniques. However, this scheme has the disadvantage of instability when the shape parameter ɛ approaches to small value. In order to deal with this issue, we adopt RBF-QR scheme that provides the higher accuracy and stable computations for small values ɛ. Two examples are presented to show the high accuracy of the method and to compare with other techniques in the literature.

Suggested Citation

  • Nikan, O. & Avazzadeh, Z., 2022. "A locally stabilized radial basis function partition of unity technique for the sine–Gordon system in nonlinear optics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 394-413.
    • Handle: RePEc:eee:matcom:v:199:y:2022:i:c:p:394-413
    DOI: 10.1016/j.matcom.2022.04.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422001483
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.04.006?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. Nikan, O. & Avazzadeh, Z. & Tenreiro Machado, J.A., 2021. "Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Cavoretto, Roberto & De Rossi, Alessandra, 2020. "Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    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. Cavoretto, Roberto & De Rossi, Alessandra, 2020. "Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methods," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    3. Cavoretto, R. & De Rossi, A. & Perracchione, E., 2023. "Learning with Partition of Unity-based Kriging Estimators," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Nikan, O. & Avazzadeh, Z., 2021. "A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics," Applied Mathematics and Computation, Elsevier, vol. 401(C).

    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:199:y:2022:i:c:p:394-413. 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.