The mathieu differential equation and generalizations to infinite fractafolds
The mathieu differential equation and generalizations to infinite fractafolds
复制标题
DOI：
10.3934/cpaa.2020073
复制
发表时间：
2019-04
影响因子：
1
通讯作者：
Shiping Cao;A. Coniglio;Xueyan Niu;R. Rand;R. Strichartz
中科院分区：
文献类型：
--
作者：
Shiping Cao;A. Coniglio;Xueyan Niu;R. Rand;R. Strichartz
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by converting the equation into an infinite system of linear equations for the Fourier coefficients. We study the asymptotic behavior of these Fourier coefficients and discuss the ways in which to numerically approximate solutions. We present both theoretical and numerical results pertaining to the stability of the Mathieu differential equation and the properties of solutions. Further, based on the idea of using Fourier series, we provide a method in which the Mathieu differential equation can be generalized to be defined on the infinite Sierpinski gasket. We discuss the stability of solutions to this fractal differential equation and describe further results concerning properties and behavior of these solutions.
