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

作者：Christodoulou Dimitris M; Graham Eagle James; Katatbeh Qutaibeh D^*

来源：Advances in Difference Equations, 2016, 2016(1): 48.

DOI：10.1186/s13662-016-0774-x

• oscillations
• second-order linear differential equations
• analytical theory
• transformations

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.

• 出版日期2016-2-15