Time integration of dissipative stochastic PDEs

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-04-01 Epub Date: 2025-11-17 DOI:10.1016/j.apnum.2025.11.005

Helena Biščević , Raffaele D’Ambrosio

引用次数: 0

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 through 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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耗散随机偏微分方程的时间积分

本文主要研究随机反应扩散问题的数值解。特别注意的是均方耗散守恒在时间积分的空间离散问题，通过有限差分获得。分析突出了随机θ-方法和随机θ-IMEX方法的保守性，强调了空间和时间步长的作用。给出了数值实验的选择，证实了理论预期。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.