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A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation

Author

Listed:
  • Qin, Hongyu
  • Wu, Fengyan
  • Ding, Deng

Abstract

We develop a linearized compact alternating direction implicit (ADI) numerical method to solve the nonlinear delayed Schrödinger equation in two-dimensional space. By discrete energy estimate method, we analyse the convergence of the fully-discrete numerical method, and show that the numerical scheme is of order O(Δt2+h4) with time stepsize Δt and space stepsize h. At last, we present several numerical examples to confirm theoretical analyses.

Suggested Citation

  • Qin, Hongyu & Wu, Fengyan & Ding, Deng, 2022. "A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006640
    DOI: 10.1016/j.amc.2021.126580
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    References listed on IDEAS

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    1. Zhang, Qifeng & Chen, Mengzhe & Xu, Yinghong & Xu, Dinghua, 2018. "Compact θ-method for the generalized delay diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 357-369.
    2. Zou, Guang-an & Wang, Bo & Sheu, Tony W.H., 2020. "On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 122-134.
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