A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation

Buyang Li; Yifei Wu

doi:10.1007/s00211-021-01226-3

A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation

Buyang Li, Yifei Wu

Research output: Journal article publication › Journal article › Academic research › peer-review

30 Citations (Scopus)

Abstract

A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schrödinger equation. The method can be implemented by using fast Fourier transform with O(Nln N) operations at every time level, and is proved to have an L²-norm error bound of O(τln(1/τ)+N-1) for H¹ initial data, without requiring any CFL condition, where τ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively.

Original language	English
Pages (from-to)	151-183
Number of pages	33
Journal	Numerische Mathematik
Volume	149
Issue number	1
Early online date	21 Aug 2021
DOIs	https://doi.org/10.1007/s00211-021-01226-3
Publication status	Published - Sept 2021

Keywords

Fast Fourier transform
First-order convergence
Low regularity
Nonlinear Schrödinger equation
Numerical solution

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1007/s00211-021-01226-3

http://hdl.handle.net/10397/93851

Cite this

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title = "A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schr{\"o}dinger equation",

abstract = "A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schr{\"o}dinger equation. The method can be implemented by using fast Fourier transform with O(Nln N) operations at every time level, and is proved to have an L2-norm error bound of O(τln(1/τ)+N-1) for H1 initial data, without requiring any CFL condition, where τ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively.",

keywords = "Fast Fourier transform, First-order convergence, Low regularity, Nonlinear Schr{\"o}dinger equation, Numerical solution",

author = "Buyang Li and Yifei Wu",

note = "Funding Information: The work of B. Li is partially supported by Projects P0031035 ZZKQ and P0030125 ZZKK at The Hong Kong Polytechnic University. The work of Y. Wu is partially supported by NSFC 11771325 and 11571118. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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N2 - A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schrödinger equation. The method can be implemented by using fast Fourier transform with O(Nln N) operations at every time level, and is proved to have an L2-norm error bound of O(τln(1/τ)+N-1) for H1 initial data, without requiring any CFL condition, where τ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively.

AB - A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schrödinger equation. The method can be implemented by using fast Fourier transform with O(Nln N) operations at every time level, and is proved to have an L2-norm error bound of O(τln(1/τ)+N-1) for H1 initial data, without requiring any CFL condition, where τ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively.

KW - Fast Fourier transform

KW - First-order convergence

KW - Low regularity

KW - Nonlinear Schrödinger equation

KW - Numerical solution

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DO - 10.1007/s00211-021-01226-3

M3 - Journal article

AN - SCOPUS:85112117816

SN - 0029-599X

VL - 149

SP - 151

EP - 183

JO - Numerische Mathematik

JF - Numerische Mathematik

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ER -

A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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