随机微分方程的数值积分：重新审视的Heun算法和Itô-Stratonovich微积分。

IF 2 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Entropy Pub Date : 2025-08-28 DOI:10.3390/e27090910

Riccardo Mannella

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引用次数: 0

摘要

广泛使用的随机微分方程（SDEs）数值积分的Heun算法被严格地重新检查。我们讨论和评估了几种可选的实现，其动机是标准Heun方案是由低阶积分器构造的。通过广泛的数值模拟评估了这些替代方案的收敛性、稳定性和平衡性。我们的研究结果证实，由于其鲁棒性，标准Heun方案仍然是SDEs的基准集成算法。作为这一分析的副产品，我们也反驳了先前在文献中关于Heun格式的强收敛性的说法。

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Numerical Integration of Stochastic Differential Equations: The Heun Algorithm Revisited and the Itô-Stratonovich Calculus.

The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and equilibrium properties of these alternatives are assessed through extensive numerical simulations. Our results confirm that the standard Heun scheme remains a benchmark integration algorithm for SDEs due to its robust performance. As a byproduct of this analysis, we also disprove a previous claim in the literature regarding the strong convergence of the Heun scheme.

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来源期刊

Entropy PHYSICS, MULTIDISCIPLINARY-

CiteScore

4.90

自引率

11.10%

发文量

1580

审稿时长

21.05 days

期刊介绍： Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.