IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v496y2025ics0096300325000876.html
   My bibliography  Save this article

Two high-order compact finite difference schemes for solving the nonlinear generalized Benjamin-Bona-Mahony-Burgers equation

Author

Listed:
  • Wang, Shengdi
  • Ma, Tingfu
  • Wu, Lili
  • Yang, Xiaojia

Abstract

In this paper, two numerical methods for solving the initial boundary value problem of one-dimensional nonlinear Generalized Benjamin-Borne-Mahony-Burgers equation are presented. Both methods utilize a fourth-order backward difference scheme for the discretization of the first-order derivative in the time direction, and apply a fourth-order compact difference scheme and a fourth-order Padé scheme to discretize the second-order and first-order spatial derivatives, respectively. The primary difference between the two methods lies in their distinct linearization strategies for the nonlinear term, which results in the formation of two linear systems. Both methods achieve fourth-order convergence in time and space. Subsequently, theoretical proofs are provided for the conservation property, stability and the existence and uniqueness of the numerical solution of the proposed numerical scheme. Finally, numerical experiments are conducted to verify the reliability and effectiveness of both methods.

Suggested Citation

  • Wang, Shengdi & Ma, Tingfu & Wu, Lili & Yang, Xiaojia, 2025. "Two high-order compact finite difference schemes for solving the nonlinear generalized Benjamin-Bona-Mahony-Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 496(C).
    • Handle: RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000876
    DOI: 10.1016/j.amc.2025.129360
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325000876
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129360?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    2. Bruzón, M.S. & Garrido, T.M. & de la Rosa, R., 2016. "Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 578-583.
    3. S. Kutluay & A. Esen, 2006. "A finite difference solution of the regularized long-wave equation," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-14, March.
    4. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.
    5. Zarebnia, M. & Parvaz, R., 2016. "On the numerical treatment and analysis of Benjamin–Bona–Mahony–Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 79-88.
    6. Changna Lu & Qianqian Gao & Chen Fu & Hongwei Yang, 2017. "Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-11, November.
    7. 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.
    8. Hai-tao Che & Xin-tian Pan & Lu-ming Zhang & Yi-ju Wang, 2012. "Numerical Analysis of a Linear‐Implicit Average Scheme for Generalized Benjamin‐Bona‐Mahony‐Burgers Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    9. Hai-tao Che & Xin-tian Pan & Lu-ming Zhang & Yi-ju Wang, 2012. "Numerical Analysis of a Linear-Implicit Average Scheme for Generalized Benjamin-Bona-Mahony-Burgers Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, March.
    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. 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).
    2. Ngondiep, Eric, 2024. "A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 560-577.
    3. Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    4. 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.
    5. Teeranush Suebcharoen & Kanyuta Poochinapan & Ben Wongsaijai, 2022. "Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    6. Hajishafieiha, J. & Abbasbandy, S., 2020. "A new class of polynomial functions for approximate solution of generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    7. Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
    8. Hajiketabi, M. & Casas, F., 2020. "Numerical integrators based on the Magnus expansion for nonlinear dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    9. Tongshuai Liu & Huanhe Dong, 2019. "The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    10. 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).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:apmaco:v:496:y:2025:i:c:s0096300325000876. 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.