A program for predicting the intervals of oscillations in the solutions of ordinary second-order linear homogeneous differential equations

Advances in Difference Equations

James Graham-Eagle¹  Dimitris M Christodoulou¹  Qutaibeh D Katatbeh² 

[1] Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, USA;Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

关键词: oscillations;    second-order linear differential equations;    analytical theory;    transformations;    34A25;    34A30;   

DOI  :  10.1186/s13662-016-0774-x

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY