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Analysis of a Chebyshev-type pseudo-spectral scheme for the nonlinear Schrödinger equation

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  • Shindin, Sergey
  • Parumasur, Nabendra
  • Govinder, Saieshan

Abstract

In this paper, we derive several error estimates that are pertinent to the study of Chebyshev-type spectral approximations on the real line. The results are applied to construct a stable and accurate pseudo-spectral Chebyshev scheme for the nonlinear Schrödinger equation. The new technique has several computational advantages as compared to Fourier and Hermite-type spectral schemes, described in the literature (see e.g., [1]–[3]. Similar to Hermite-type methods, we do not require domain truncation and/or use of artificial boundary conditions. At the same time, the computational complexity is comparable to the best Fourier-type spectral methods described in the literature.

Suggested Citation

  • Shindin, Sergey & Parumasur, Nabendra & Govinder, Saieshan, 2017. "Analysis of a Chebyshev-type pseudo-spectral scheme for the nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 271-289.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:271-289
    DOI: 10.1016/j.amc.2017.03.005
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    Cited by:

    1. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.
    2. Mohammadi, Reza, 2018. "Smooth Quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 204-215.

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