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Analysis of a split...
Analysis of a splitting scheme for a class of nonlinear stochastic Schrodinger equations
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- Brehier, C. E. (author)
- Université Claude-Bernard Lyon 1,Claude Bernard University Lyon 1
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- Cohen, David (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Umeå universitet,Umeå University,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- Elsevier BV, 2023
- 2023
- English.
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In: Applied Numerical Mathematics. - : Elsevier BV. - 0168-9274. ; 186, s. 57-83
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Abstract
Subject headings
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- We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrodinger equations driven by additive 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 (trace formula). 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. (c) 2023 The Author(s). Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Stochastic partial differential equations
- Stochastic Schrodinger
- equations
- Splitting integrators
- Strong convergence
- Geometric
- numerical integration
- Trace formulas
- partial-differential-equations
- convergence-rates
- hamiltonian-systems
- semidiscrete scheme
- wigner-poisson
- integrators
- time
- conservation
- order
- wave
- Mathematics
- Geometric numerical integration
Publication and Content Type
- ref (subject category)
- art (subject category)
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