文章基本信息

标题：A program for predicting the intervals of oscillations in the solutions of ordinary second-order linear homogeneous differential equations
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作者：Dimitris M Christodoulou ; James Graham-Eagle ; Qutaibeh D Katatbeh 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：48
DOI：10.1186/s13662-016-0774-x
语种：English
出版社：Hindawi Publishing Corporation
摘要：We derive a new criterion for deducing the intervals of oscillatory behavior in the solutions of ordinary second-order linear homogeneous differential equations from their coefficients. The validity of the method depends on one’s ability to transform a given differential equation to its simplest possible form, so a program must be executed that involves transformations of both variables before the criterion can be applied. The payoff of the program is the detection of oscillations precisely where they may occur in finite or infinite intervals of the independent variable. We demonstrate how the oscillation-detection program can be carried out for a variety of well-known differential equations from applied mathematics and mathematical physics.
关键词：oscillations ; second-order linear differential equations ; analytical theory ; transformations