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On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations

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  • Ran, Yu-Hong
  • Wang, Jun-Gang
  • Wang, Dong-Ling

Abstract

The implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable, is employed to discretize the space fractional coupled nonlinear Schrödinger equations. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix which can be written as the imaginary unit times the identity matrix and a symmetric diagonal-plus-Toeplitz matrix. In this paper, the HSS-like iteration method is proposed to solve the discretized linear system. Theoretical analyses show that the HSS-like iteration method is unconditionally convergent. Numerical examples are presented to illustrate the effectiveness of the HSS-like iteration method.

Suggested Citation

  • Ran, Yu-Hong & Wang, Jun-Gang & Wang, Dong-Ling, 2015. "On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 482-488.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:482-488
    DOI: 10.1016/j.amc.2015.09.028
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    References listed on IDEAS

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    1. Wang, Dongling & Xiao, Aiguo & Yang, Wei, 2015. "Maximum-norm error analysis of a difference scheme for the space fractional CNLS," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 241-251.
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    Cited by:

    1. Li, Hui & Jiang, Wei & Li, Wenya, 2019. "Space-time spectral method for the Cattaneo equation with time fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 325-336.

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