Abstract
In this paper, we address our investigation to the numerical integration of nonlinear stochastic differential equations exhibiting a mean-square contractive character along the exact dynamics. We specifically focus on the conservation of this qualitative feature along the discretized dynamics originated by applying stochastic \(\vartheta \)-methods. Retaining the mean-square contractivity under time discretization is translated into a proper stepsize restriction. Here we analyze the choice of the optimal parameter \(\vartheta \) making this restriction less demanding and, at the same time, maximizing the stability interval. A numerical evidence is provided to confirm our theoretical results.
This work is supported by GNCS-INDAM project and by PRIN2017-MIUR project 2017JYCLSF “Structure preserving approximation of evolutionary problems”.
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D’Ambrosio, R., Di Giovacchino, S. (2021). Optimal \(\vartheta \)-Methods for Mean-Square Dissipative Stochastic Differential Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_9
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