建模仍然很重要：数学生物学中灾难性浮点错误的一个令人惊讶的实例和ode的数值方法

IF 6.1 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2025-08-07 DOI:10.1137/23m1563967

Cordula Reisch, Hendrik Ranocha

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引用次数: 0

摘要

SIAM评论，第67卷，第3期，624-641页，2025年8月。摘要。我们引导读者通过数学建模和数值分析的旅程，强调这两个学科的关键相互作用。针对具有动力系统和常微分方程数值方法基础知识的本科生，我们探索了一个数学生物学模型，其中数值方法由于灾难性的浮点误差而严重失败。我们通过研究模型的稳态来分析这种行为的原因，并使用不变量理论来开发适合数值模拟的替代模型。我们的故事旨在激发分析知识和数值知识的结合，即使在那些世界乍一看很好的情况下。我们已经建立了一个在线存储库，其中包含了本文中所有数值实验的交互式笔记本，以使该研究完全可复制并对课堂教学有用。

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Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs

SIAM Review, Volume 67, Issue 3, Page 624-641, August 2025.
Abstract.We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge of dynamical systems and numerical methods for ordinary differential equations, we explore a model from mathematical biology where numerical methods fail badly due to catastrophic floating point errors. We analyze the reasons for this behavior by studying the steady states of the model and use the theory of invariants to develop an alternative model suited for numerical simulations. Our story is intended to motivate the combining of analytical knowledge and numerical knowledge, even in those cases where the world looks fine at first sight. We have set up an online repository containing an interactive notebook with all the numerical experiments in this article to make this study fully reproducible and useful for classroom teaching.

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.