1. Analysis of a Chebyshev-type pseudo-spectral scheme for the nonlinear Schrödinger equation.
- Author
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Shindin, Sergey, Parumasur, Nabendra, and Govinder, Saieshan
- Subjects
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CHEBYSHEV approximation , *NONLINEAR Schrodinger equation , *ERROR analysis in mathematics , *ESTIMATION theory , *POLYNOMIALS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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