Abstract
The aim of this paper is the analysis of exponential mean-square stability properties of nonlinear stochastic linear multistep methods. In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential mean-square contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand whether a stochastic linear multistep method can provide an analogous behaviour and which restrictions on the employed stepsize should be imposed in order to reproduce the contractive behaviour. Numerical experiments confirming the theoretical analysis are also given.
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18 October 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10444-021-09901-7
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Acknowledgements
The second author is member of the GNCS-INDAM group. The authors are thankful to the anonymous reviewers for their precious comments.
Funding
Open access funding provided by Università degli Studi dell’Aquila within the CRUI-CARE Agreement. This work is supported by GNCS-INDAM project and by PRIN2017-MIUR project 2017JYCLSF “Structure preserving approximation of evolutionary problems”.
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Communicated by: Ivan Oseledets
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Buckwar, E., D’Ambrosio, R. Exponential mean-square stability properties of stochastic linear multistep methods. Adv Comput Math 47, 55 (2021). https://doi.org/10.1007/s10444-021-09879-2
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DOI: https://doi.org/10.1007/s10444-021-09879-2
Keywords
- Exponential mean-square stability
- Exponential mean-square contractivity
- Nonlinear stochastic differential equations
- Stochastic linear multistep methods
- Nonlinear stability