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Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme

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  • Wang, Tingchun
  • Nie, Tao
  • Zhang, Luming
  • Chen, Fangqi

Abstract

This article describes a finite difference scheme which is linearly uncoupled in computation for a nonlinearly coupled Schrödinger system. This numerical scheme is proved to preserve the original conservative properties. Using the discrete energy analysis method, we also prove that the scheme is unconditionally stable and second-order convergent in discrete L2-norm based on some preliminary estimations. The results show that the new scheme is efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:607-621
    DOI: 10.1016/j.matcom.2008.03.017
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    References listed on IDEAS

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    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. 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.
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