Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations
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| Titel: | Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations |
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| Autoren: | Bréhier, Charles-Edouard, Cohen, David, 1977 |
| Quelle: | Numerisk analys och simulering av PDE med slumpmässig dispersion Applied Numerical Mathematics. 186:57-83 |
| Schlagwörter: | Geometric numerical integration, Stochastic partial differential equations, Strong convergence, Trace formulas, Stochastic Schrödinger equations, Splitting integrators |
| Beschreibung: | We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive Itô noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times. On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme. |
| Dateibeschreibung: | electronic |
| Zugangs-URL: | https://research.chalmers.se/publication/534303 https://research.chalmers.se/publication/527569 https://arxiv.org/abs/2007.02354 |
| Datenbank: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive Itô noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times. On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme. |
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| ISSN: | 01689274 |
| DOI: | 10.1016/j.apnum.2023.01.002 |