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Exponential integra...
Exponential integrators for stochastic Schrödinger equations driven by Itô noise
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- Anton, Rikard (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University
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- Cohen, David (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Department of Mathematics, University of Innsbruck, A–6020 Innsbruck, Austria,Umeå University
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(creator_code:org_t)
- 2018-06
- 2018
- English.
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In: Journal of Computational Mathematics. - : Global Science Press. - 0254-9409 .- 1991-7139. ; 36:2, s. 276-309
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Stochastic partial differential equations
- Stochastic Schr¨odinger equations
- Numerical methods
- Geometric numerical integration
- Stochastic exponential integrators
- Strong convergence
- Trace formulas
Publication and Content Type
- ref (subject category)
- art (subject category)
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