IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v289y2016icp159-171.html
   My bibliography  Save this article

Solitary-wave solutions of the GRLW equation using septic B-spline collocation method

Author

Listed:
  • Karakoç, S. Battal Gazi
  • Zeybek, Halil

Abstract

In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different linearization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L2 and L∞ and the invariants I1, I2 and I3. A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numerical scheme is preferable to some recent numerical schemes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:159-171
    DOI: 10.1016/j.amc.2016.05.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303307
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.05.021?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. Dumbser, M. & Facchini, M., 2016. "A space-time discontinuous Galerkin method for Boussinesq-type equations," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 336-346.
    2. Hammad, D.A. & El-Azab, M.S., 2015. "A 2N order compact finite difference method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 248-261.
    3. Soliman, A.A., 2005. "Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 119-124.
    4. Hamdi, S. & Enright, W.H. & Schiesser, W.E & Gottlieb, J.J., 2004. "Exact solutions and invariants of motion for general types of regularized long wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 535-545.
    5. Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
    6. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
    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. Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.
    2. Hammad, D.A. & El-Azab, M.S., 2016. "Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 228-240.
    3. Fuchang Zheng & Shuhong Bao & Yulan Wang & Shuguang Li & Zhiyuan Li, 2017. "A Good Numerical Method for the Solution of Generalized Regularized Long Wave Equation," Modern Applied Science, Canadian Center of Science and Education, vol. 11(6), pages 1-72, June.
    4. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    5. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    6. Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
    7. Gao, Fuzheng & Qiao, Feng & Rui, Hongxing, 2015. "Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 64-73.
    8. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
    9. Wang, Xiaofeng & Dai, Weizhong & Guo, Shuangbing, 2019. "A conservative linear difference scheme for the 2D regularized long-wave equation," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 55-70.
    10. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    11. Yang, Xiaojia & Ge, Yongbin & Zhang, Lin, 2019. "A class of high-order compact difference schemes for solving the Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 394-417.
    12. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    13. Yang, Xiaojia & Ge, Yongbin & Lan, Bin, 2021. "A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 510-534.
    14. Demiray, Hilmi, 2009. "Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1578-1586.
    15. Cosgun, Tahir & Sari, Murat, 2020. "Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(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:289:y:2016:i:c:p:159-171. 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.