NUMERICAL ANALYSIS ON THE SIERPINSKI GASKET, WITH APPLICATIONS TO SCHRÖDINGER EQUATIONS, WAVE EQUATION, AND GIBBS' PHENOMENON-Reference-Cited by-同舟云学术

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

Published:2004-12 Issue:04 Volume:12 Page:413-449
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

COLETTA KEVIN¹,DIAS KEALEY²,STRICHARTZ ROBERT S.³

Affiliation:

1. Mathematics Department, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

2. Mathematics Department, The State University of New York, Stony Brook, NY 11794, USA

3. Mathematics Department, Malott Hall, Cornell University, Ithaca, NY 14853, USA

Abstract

We show how to improve the finite element method on the Sierpinski gasket (SG) to allow arbitrary partitions of the space. We use this method to study numerically solutions of the Schrödinger equation with well-type potentials, and the wave equation. We also show that Fourier series-type expansions on SG of functions with jump discontinuities appear to exhibit a self-similar Gibbs' phenomenon.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X04002689

Reference16 articles.

1. Analysis on Fractals

2. Diffusions on fractals

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