Randomized exponential integrators for modulated nonlinear Schrodinger equations

Hofmanová M, Knoeller M, Schratz K (2020)
IMA Journal of Numerical Analysis 40(4): 2143-2162.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Hofmanová, MartinaUniBi; Knoeller, Marvin; Schratz, Katharina
Abstract / Bemerkung
We consider the nonlinear Schrodinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class W-alpha,W-2 for some alpha is an element of (0, 1). Due to the loss of smoothness in the problem, classical numerical methods face severe order reduction. In this work, we develop and analyze a new randomized exponential integrator based on a stratifiedMonte Carlo approximation. The new discretization technique averages the high oscillations in the solution allowing for improved convergence rates of order alpha + 1/2. In addition, the new approach allows us to treat a far more general class of modulations than the available literature. Numerical results underline our theoretical findings and show the favorable error behavior of our new scheme compared to classical methods.
Stichworte
randomized exponential integrator; modulated Schrodinger; error analysis
Erscheinungsjahr
2020
Zeitschriftentitel
IMA Journal of Numerical Analysis
Band
40
Ausgabe
4
Seite(n)
2143-2162
ISSN
0272-4979
eISSN
1464-3642
Page URI
https://pub.uni-bielefeld.de/record/2951313

Zitieren

Hofmanová M, Knoeller M, Schratz K. Randomized exponential integrators for modulated nonlinear Schrodinger equations. IMA Journal of Numerical Analysis. 2020;40(4):2143-2162.
Hofmanová, M., Knoeller, M., & Schratz, K. (2020). Randomized exponential integrators for modulated nonlinear Schrodinger equations. IMA Journal of Numerical Analysis, 40(4), 2143-2162. doi:10.1093/imanum/drz050
Hofmanová, M., Knoeller, M., and Schratz, K. (2020). Randomized exponential integrators for modulated nonlinear Schrodinger equations. IMA Journal of Numerical Analysis 40, 2143-2162.
Hofmanová, M., Knoeller, M., & Schratz, K., 2020. Randomized exponential integrators for modulated nonlinear Schrodinger equations. IMA Journal of Numerical Analysis, 40(4), p 2143-2162.
M. Hofmanová, M. Knoeller, and K. Schratz, “Randomized exponential integrators for modulated nonlinear Schrodinger equations”, IMA Journal of Numerical Analysis, vol. 40, 2020, pp. 2143-2162.
Hofmanová, M., Knoeller, M., Schratz, K.: Randomized exponential integrators for modulated nonlinear Schrodinger equations. IMA Journal of Numerical Analysis. 40, 2143-2162 (2020).
Hofmanová, Martina, Knoeller, Marvin, and Schratz, Katharina. “Randomized exponential integrators for modulated nonlinear Schrodinger equations”. IMA Journal of Numerical Analysis 40.4 (2020): 2143-2162.

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arXiv: 1711.01091

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