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

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 ( N ln N ) operations at every time level, and is proved to have an L 2 -norm error...

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Bibliographic Details
Published in:Numerische Mathematik Vol. 149; no. 1; pp. 151 - 183
Main Authors: Li, Buyang, Wu, Yifei
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021
Springer Nature B.V
Subjects:
Fast Fourier transformations
Fourier transforms
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Regularity
Schrodinger equation
Simulation
Theoretical
65M15
Low regularity
Numerical solution
First-order convergence
Fast Fourier transform
35Q55
Nonlinear Schrödinger equation
65M12
ISSN:0029-599X, 0945-3245
Online Access:Get full text
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Summary: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 ( N ln N ) operations at every time level, and is proved to have an L 2 -norm error bound of O ( τ ln ( 1 / τ ) + N - 1 ) for H 1 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.
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ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-021-01226-3