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arXiv · 2507.16658

Time integration of dissipative stochastic PDEs

Helena Biščević·Raffaele D'Ambrosio
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Abstract

The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem, obtained by means of finite differences. The analysis highlights the conservative ability of stochastic $θ$-methods and stochastic $θ$-IMEX methods, emphasizing the roles of spatial and temporal stepsizes. A selection of numerical experiments is provided, confirming the theoretical expectations.

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Helena Biščević, Raffaele D'Ambrosio. 2025-07-22. Time integration of dissipative stochastic PDEs. https://arxiv.org/abs/2507.16658

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