کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4643381 1341378 2006 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Computing eigenfunctions on the Koch Snowflake: A new grid and symmetry
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Computing eigenfunctions on the Koch Snowflake: A new grid and symmetry
چکیده انگلیسی

In this paper, we numerically solve the eigenvalue problem Δu+λu=0Δu+λu=0 on the fractal region defined by the Koch Snowflake, with zero-Dirichlet or zero-Neumann boundary conditions. The Laplacian with boundary conditions is approximated by a large symmetric matrix. The eigenvalues and eigenvectors of this matrix are computed by ARPACK. We impose the boundary conditions in a way that gives improved accuracy over the previous computations of Lapidus, Neuberger, Renka and Griffith. We extrapolate the results for grid spacing h   to the limit h→0h→0 in order to estimate eigenvalues of the Laplacian and compare our results to those of Lapidus et al. We analyze the symmetry of the region to explain the multiplicity-two eigenvalues, and present a canonical choice of the two eigenfunctions that span each two-dimensional eigenspace.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 191, Issue 1, 15 June 2006, Pages 126–142
نویسندگان
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