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Exponential integrators for stochastic Schrödinger equations driven by Itô noisePrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 36, no 2, p. 276-309Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Global Science Press, 2018. Vol. 36, no 2, p. 276-309
##### Keywords [en]

Stochastic partial differential equations, Stochastic Schr¨odinger equations, Numerical methods, Geometric numerical integration, Stochastic exponential integrators, Strong convergence, Trace formulas
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-137247DOI: 10.4208/jcm.1701-m2016-0525OAI: oai:DiVA.org:umu-137247DiVA, id: diva2:1117102
#####

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##### Funder

Swedish Research Council, 2013-4562Available from: 2017-06-28 Created: 2017-06-28 Last updated: 2018-06-09Bibliographically approved
##### In thesis

We study an explicit exponential scheme for the time discretisation of stochastic Schr¨odinger Equations Driven by additive or Multiplicative Itô Noise. The numerical scheme is shown to converge with strong order 1 if the noise is additive and with strong order 1/2 for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of the linear stochastic Schr¨odinger equations satisfy trace formulas for the expected mass, energy, and momentum (i. e., linear drifts in these quantities). Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.

1. Exponential integrators for stochastic partial differential equations$(function(){PrimeFaces.cw("OverlayPanel","overlay1200403",{id:"formSmash:j_idt726:0:j_idt730",widgetVar:"overlay1200403",target:"formSmash:j_idt726:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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