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Exponential Integrators for Stochastic Schrödinger Equations Driven by Itô Noise

Exponential Integrators for Stochastic Schrödinger Equations Driven by Itô Noise
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Year:    2018

Author:    Rikard Anton, David Cohen

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 2 : pp. 276–309

Abstract

We study an explicit exponential scheme for the time discretisation of stochastic Schrödinger 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 Schrödinger 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1701-m2016-0525

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 2 : pp. 276–309

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Stochastic partial differential equations Stochastic Schrödinger equations Numerical methods Geometric numerical integration Stochastic exponential integrators Strong convergence Trace formulas.

Author Details

Rikard Anton

David Cohen

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