A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation

Alexander Ostermann; Fangyan Yao

doi:10.1007/s10915-022-01786-y

journal article Feb 22, 2022

A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation

Alexander Ostermann

Fangyan Yao

Journal of Scientific Computing Vol. 91 No. 1 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/s10915-022-01786-y

Topics

No keywords indexed for this article. Browse by subject →

References

13

[1]

Besse, C., Bidégaray, B., Descombes, S.: Order estimates in time of splitting methods for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 40, 26–40 (2002) 10.1137/s0036142900381497

[2]

Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3, 107–156 (1993) 10.1007/bf01896020

[3]

Faou, E.: Geometric Numerical Integration and Schrödinger Equations. European Mathematical Society Publishing House, Zürich (2012) 10.4171/100

[4]

Jahnke, T., Lubich, C.: Error bounds for exponential operator splittings. BIT 40, 735–744 (2000) 10.1023/a:1022396519656

[5]

Kato, T., Ponce, G.: Commutator estimates and the Euler and Navier–Stokes equations. Commun. Pure Appl. Math. 41, 891–907 (1988) 10.1002/cpa.3160410704

[6]

Knöller, M., Ostermann, A., Schratz, K.: A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data. SIAM J. Numer. Anal. 57, 1967–1986 (2019) 10.1137/18m1198375

[7]

Li, B., Wu, Y.: A full discrete low-regularity integrator for the 1D period cubic nonlinear Schrödinger equation. Numer. Math. 149, 151–183 (2021) 10.1007/s00211-021-01226-3

[8]

Lubich, C.: On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Math. Comp. 77, 2141–2153 (2008) 10.1090/s0025-5718-08-02101-7

[9]

Ostermann, A., Schratz, K.: Low regularity exponential-type integrators for semilinear Schrödinger equations. Found. Comput. Math. 18, 731–755 (2018) 10.1007/s10208-017-9352-1

[10]

Ostermann, A., Rousset, F., Schratz, K.: Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Found. Comput. Math. 21, 725–765 (2021) 10.1007/s10208-020-09468-7

[11]

Ostermann, A., Rousset, F., Schratz, K.: Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces, accepted for publication in J. Eur. Math. Soc.

[12]

Sanz-Serna, J.M.: Methods for the numerical solution of the nonlinear Schrödinger equation. Math. Comp. 43, 21–27 (1984) 10.1090/s0025-5718-1984-0744922-x

[13]

Wu, Y., Yao, F.: A first-order Fourier integrator for the nonlinear Schrödinger equation on $${\mathbb{T}}$$ without loss of regularity, accepted for publication in Math. Comp.

Metrics

11

Citations

13

References

Details

Published: Feb 22, 2022
Vol/Issue: 91(1)
License: View

Authors

Funding

National Natural Science Foundation of China Award: 11831003

Cite This Article

Alexander Ostermann, Fangyan Yao (2022). A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation. Journal of Scientific Computing, 91(1). https://doi.org/10.1007/s10915-022-01786-y

A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation

You May Also Like