经典边界层问题中的意外值

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2021-07-24 DOI:10.1137/21M1436087

W. Clark, Mario W. Gomes, A. Rodriguez-Gonzalez, L. Stein, S. Strogatz

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引用次数: 2

摘要

我们重新审视一个课本上的奇异摄动非线性边值问题的例子。出乎意料的是，它显示了许多以前似乎被忽视的现象，包括当一个人改变小参数时解的数量的干草叉分叉，以及可以用基本方法计算的初始条件中的超小项。根据我们自己的课堂经验，我们相信这个问题可以为学生在微扰方法、应用动力系统或数值分析课程中提供一个愉快的练习。

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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Surprises in a Classic Boundary-Layer Problem

We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of solutions as one varies the small parameter, and transcendentally small terms in the initial conditions that can be calculated by elementary means. Based on our own classroom experience, we believe this problem could provide an enjoyable workout for students in courses on perturbation methods, applied dynamical systems, or numerical analysis.

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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.