IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v394y2021ics0096300320307402.html
   My bibliography  Save this article

A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations

Author

Listed:
  • Oruç, Ömer

Abstract

In this study, we examine numerical solutions of Zakharov–Rubenchik system which is a coupled nonlinear partial differential equation. The numerical method in the current study is based on radial basis function finite difference (RBF-FD) meshless method and an explicit Runge–Kutta method. As a radial basis function we choose polyharmonic spline augmented with polynomials. The essential motivation for choosing polyharmonic spline is that it is free of shape parameter which has a crucial role in accuracy and stability of meshless methods. The main benefit of the proposed method is the approximation of the differential operators is performed on local-support domain which produces sparse differentiation matrices. This reduces computational cost remarkably. To see performance of the proposed method, some test problems are solved. L∞ error norms and conserved quantities such as mass and energy are calculated. Numerical outcomes are presented and compared with other methods available in the literature. From the comparison it can be deduced that the proposed method gives reliable and precise results with low computational cost. Stability of the proposed method is also discussed.

Suggested Citation

  • Oruç, Ömer, 2021. "A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307402
    DOI: 10.1016/j.amc.2020.125787
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320307402
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125787?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. Su, LingDe, 2019. "A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 232-247.
    2. Hajiketabi, M. & Abbasbandy, S. & Casas, F., 2018. "The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation in arbitrary domains," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 223-243.
    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. Jiwari, Ram, 2022. "Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 106-126.

    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. Yang Yu & Xiaochuan Luo & Huaxi (Yulin) Zhang & Qingxin Zhang, 2019. "The Solution of Backward Heat Conduction Problem with Piecewise Linear Heat Transfer Coefficient," Mathematics, MDPI, vol. 7(5), pages 1-17, April.
    2. Hajiketabi, M. & Casas, F., 2020. "Numerical integrators based on the Magnus expansion for nonlinear dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Zakieh Avazzadeh & Omid Nikan & José A. Tenreiro Machado, 2020. "Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    4. Xubiao He & Pu Gong, 2020. "A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 999-1019, March.
    5. Yue, Xiaohui & Shao, Xingling & Li, Jie, 2021. "Prescribed chattering reduction control for quadrotors using aperiodic signal updating," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    6. Li-Dan Hong & Cheng-Yu Ku & Chih-Yu Liu, 2022. "A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    7. Muaz Seydaoğlu, 2019. "A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    8. 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).
    9. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(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:apmaco:v:394:y:2021:i:c:s0096300320307402. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.