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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Veröffentlicht in:	Numerische Mathematik Jg. 149; H. 1; S. 151 - 183
Hauptverfasser:	Li, Buyang, Wu, Yifei
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021 Springer Nature B.V
Schlagworte:	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
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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 ( 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.
AbstractList	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. 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(NlnN) 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.
Author	Li, Buyang Wu, Yifei
Author_xml	– sequence: 1 givenname: Buyang surname: Li fullname: Li, Buyang email: buyang.li@polyu.edu.hk, libuyang@gmail.com organization: Department of Applied Mathematics, The Hong Kong Polytechnic University – sequence: 2 givenname: Yifei surname: Wu fullname: Wu, Yifei organization: Center for Applied Mathematics, Tianjin University
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Cites_doi	10.1007/s10208-017-9352-1 10.1201/9781420063646 10.1093/imanum/drz030 10.1007/s10915-013-9799-4 10.1002/cpa.3160410704 10.1017/S0962492910000048 10.1007/BF01896020 10.1007/s00211-016-0859-1 10.1090/S0025-5718-08-02101-7 10.1090/S0025-5718-1984-0744922-X 10.1137/18M1198375 10.1007/s10208-020-09468-7 10.1137/S0036142900381497 10.1016/j.jde.2011.01.028 10.4171/rmi/1049 10.1016/j.jmaa.2016.05.014 10.1093/imanum/drab054 10.1090/mcom/3557
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SubjectTerms	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
Title	A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
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