Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials

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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Bibliographic Details
Published inarXiv.org
Main Authors Andrews, Ulysses, Bonik, Grigory, Chen, Joe P, Martin, Richard W, Teplyaev, Alexander
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.07.2016
Subjects
Fractal analysis
Mathematical analysis
Mathematics - Functional Analysis
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
Mathematics - Probability
Physics - Mathematical Physics
Physics - Quantum Physics
Polynomials
Self-similarity
Wave equations
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1505.05855