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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| Vydáno v: | Numerische Mathematik Ročník 149; číslo 1; s. 151 - 183 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2021
Springer Nature B.V |
| Témata: | |
| ISSN: | 0029-599X, 0945-3245 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0029-599X 0945-3245 |
| DOI: | 10.1007/s00211-021-01226-3 |