2018
DOI: 10.1002/num.22264
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Abstract: In this article, a Fourier pseudospectral method, which preserves the conforal conservation la, is proposed for solving the damped nonlinear Schrödinger equation. Based on the energy method and the semi‐norm equivalence between the Fourier pseudospectral method and the finite difference method, a priori estimate for the new method is established, which shows that the proposed method is unconditionally convergent with order of O ( normalτ 2 + J 1 − r ) in the discrete L ∞ ‐norm, where normalτ i… Show more

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Cited by 11 publications
(8 citation statements)
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“…Additionally, the computation of the NLS is a critical part of the verification process of the analytical theories. This has been achieved in the case of non-varying coefficients, with success for a large number of comparative numerical algorithms [12][13][14][15][16].…”
Section: Introductionmentioning
confidence: 96%
“…Additionally, the computation of the NLS is a critical part of the verification process of the analytical theories. This has been achieved in the case of non-varying coefficients, with success for a large number of comparative numerical algorithms [12][13][14][15][16].…”
Section: Introductionmentioning
confidence: 96%
“…AVF method upon preserving some structure characters of a dynamic system is a suitable candidate to design energy‐preserving schemes. () It is widely used to construct structure‐preserving schemes for partial differential equations . To improve the computational efficiency, high‐order compact method aims to design high‐order schemes with smaller stencils .…”
Section: Introductionmentioning
confidence: 99%
“…For the classical NLS equations, in [10], Gong first established the semi-norm equivalence between the finite difference method and the Fourier pseudo-spectral method and thus obtained the unconditionally convergent results on the Fourier pseudo-spectral in the discrete L 2 norm. Then based on this equivalence, the error estimates of the Fourier pseudo-spectral method in the discrete L ∞ norm were obtained in [15]. However, this error analysis technique for establishing semi-norm equivalence can not extend to the FNLS equations.…”
Section: Introductionmentioning
confidence: 99%