IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v360y2019icp58-69.html
   My bibliography  Save this article

Parametric spline schemes for the coupled nonlinear Schrödinger equation

Author

Listed:
  • Lin, Bin

Abstract

In this study, the parametric cubic spline scheme is implemented to find the approximate solution of the coupled nonlinear Schrödinger equations. This scheme is based on the Crank–Nicolson method in time and parametric cubic spline functions in space. The error analysis and stability of the scheme are investigated and the numerical results show that we can get different precision schemes by choosing suitably parameter values and this scheme is unconditionally stable. Two problems are solved to illustrate the efficiency of the methods as well as to compare with other methods.

Suggested Citation

  • Lin, Bin, 2019. "Parametric spline schemes for the coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 58-69.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:58-69
    DOI: 10.1016/j.amc.2019.04.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303340
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.046?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. Ismail, M.S. & Taha, Thiab R., 2007. "A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 302-311.
    2. Ismail, M.S. & Taha, Thiab R., 2001. "Numerical simulation of coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(6), pages 547-562.
    3. 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.
    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. Iqbal, Azhar & Abd Hamid, Nur Nadiah & Md. Ismail, Ahmad Izani & Abbas, Muhammad, 2021. "Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 1-16.

    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. Ilati, Mohammad & Dehghan, Mehdi, 2019. "DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose–Einstein condensates," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 244-253.
    2. Zhou, Shenggao & Cheng, Xiaoliang, 2010. "Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2362-2373.
    3. 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.
    4. Wang, Tingchun & Nie, Tao & Zhang, Luming & Chen, Fangqi, 2008. "Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 607-621.
    5. Vyacheslav Trofimov & Maria Loginova & Mikhail Fedotov & Daniil Tikhvinskii & Yongqiang Yang & Boyuan Zheng, 2022. "Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation," Mathematics, MDPI, vol. 10(11), pages 1-24, June.
    6. Tsang, S.C. & Chow, K.W., 2004. "The evolution of periodic waves of the coupled nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 551-564.
    7. Taghread Ghannam Alharbi & Abdulghani Alharbi, 2023. "A Study of Traveling Wave Structures and Numerical Investigations into the Coupled Nonlinear Schrödinger Equation Using Advanced Mathematical Techniques," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
    8. Straughan, B., 2009. "Nonlinear acceleration waves in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 763-769.
    9. Todorov, M.D. & Christov, C.I., 2009. "Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector NLSE," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 46-55.
    10. Sonnier, W.J. & Christov, C.I., 2005. "Strong coupling of Schrödinger equations: Conservative scheme approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 514-525.
    11. Ismail, M.S. & Taha, Thiab R., 2007. "A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 302-311.

    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:360:y:2019:i:c:p:58-69. 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.