Numerical analysis on the Sierpinski gasket, with applications to Schrodinger equations, wave equation, and Gibbs' phenomenon

被引：18

作者：

Coletta, K

Dias, K

Strichartz, RS

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[2] Rensselaer Polytech Inst, Dept Math, Troy, NY 12180 USA

[3] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2004年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

Sjierpinski gasket; analysis on fractals; finite element method; Schrodinger equations; well-type potentials; wave equation; Fourier series; Gibbs' phenomenon;

D O I：

10.1142/S0218348X04002689

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Schrodinger 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.

引用

页码：413 / 449

页数：37

共 20 条

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