NUMERICAL ANALYSIS ON THE SIERPINSKI GASKET, WITH APPLICATIONS TO SCHRÖDINGER EQUATIONS, WAVE EQUATION, AND GIBBS' PHENOMENON

DOI10.1142/S0218348X04002689zbMath1304.28005MaRDI QIDQ5497003

Robert S. Strichartz, Kevin Coletta, Kealey Dias

Publication date: 30 January 2015

Published in: Fractals (Search for Journal in Brave)

zbMATH Keywords

wave equationfinite element methodSchrödinger equationsFourier seriesSierpinski gasketanalysis on fractalsGibbs' phenomenonwell-type potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fractals (28A80) Miscellaneous topics in partial differential equations (35R99)

Related Items (10)

Harmonic oscillators on infinite Sierpinski gaskets ⋮ Analysis on products of fractals ⋮ Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary ⋮ Spectral operators on the Sierpinski gasket I ⋮ One-dimensional wave equations defined by fractal Laplacians ⋮ From Strichartz Estimates to Differential Equations on Fractals ⋮ On the Gibbs phenomenon for expansions by eigenfunctions of the boundary problem for Dirac system ⋮ Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials ⋮ Orthogonal Polynomials with Respect to Self-Similar Measures ⋮ Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpiński gasket

Cites Work

• Calculus on the Sierpinski gasket. I: Polynomials, exponentials and power series
• Analysis on products of fractals
• Calculus on the Sierpinski gasket II: Point singularities, eigenfunctions, and normal derivatives of the heat kernel
• Unnamed Item

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