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.