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

Sergey Shindin, Nabendra Parumasur and Saieshan Govinder

Applied Mathematics and Computation, 2017, vol. 307, issue C, 271-289

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.

Keywords: Algebraically mapped Chebyshev polynomials; Pseudo-spectral methods; Error estimates; Schrödinger equation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:307:y:2017:i:c:p:271-289

DOI: 10.1016/j.amc.2017.03.005

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