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Parametric spline schemes for the coupled nonlinear Schrödinger equation

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    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.

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