The mathieu differential equation and generalizations to infinite fractafolds | Zendy

Shiping Cao | Zendy; Anthony Coniglio | Zendy; Xueyan Niu | Zendy; Richard H. Rand | Zendy; Robert S. Strichartz | Zendy

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The mathieu differential equation and generalizations to infinite fractafolds

Author(s) -

Shiping Cao,

Anthony Coniglio,

Xueyan Niu,

Richard H. Rand,

Robert S. Strichartz

Publication year - 2019

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2020073

Subject(s) - mathieu function , fourier series , mathematics , mathematical analysis , differential equation , first order partial differential equation , exact differential equation , fourier analysis , fourier transform , partial differential equation

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.

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