Stroboscopic averaging methods to study autoresonance and other problems with slowly varying forcing frequencies

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-04-14 DOI:10.1016/j.apnum.2025.04.004

M.P. Calvo , J.M. Sanz-Serna , Beibei Zhu

引用次数: 0

Abstract

Autoresonance is a phenomenon of physical interest that may take place when a nonlinear oscillator is forced at a frequency that varies slowly. The stroboscopic averaging method (SAM), which provides an efficient numerical technique for the integration of highly oscillatory systems, cannot be used directly to study autoresonance due to the slow changes of the forcing frequency. We study how to modify SAM to cater for such slow variations. Numerical experiments show the computational advantages of using SAM.

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频闪平均法研究自共振和其他强迫频率缓慢变化的问题

自共振是一种物理现象，当非线性振荡器被强迫以缓慢变化的频率时，可能会发生这种现象。频闪平均法（SAM）为高振荡系统的积分提供了一种有效的数值计算方法，但由于强迫频率变化缓慢，不能直接用于研究自共振。我们研究如何修改SAM以适应这种缓慢的变化。数值实验证明了采用SAM的计算优势。

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.