Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials
Ulysses Andrews, Grigory Bonik, Joe P. Chen, Richard W. Martin,, Alexander Teplyaev
TL;DR
This paper investigates the wave equation on one-dimensional fractals using spectral decimation, introducing numerical methods and analytical estimates to understand wave dynamics on complex self-similar structures.
Contribution
It develops new numerical approximation techniques and analytical estimates for the wave equation on fractals analyzed via spectral decimation.
Findings
Efficient numerical methods for wave equations on fractals
Uniform analytical estimates for wave behavior
Insights into spectral properties of fractal structures
Abstract
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by analytical methods.
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