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The distribution of the eigenvalues of the discrete Laplacian

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Abstract

We estimate the distribution of the eigenvalues of the discrete Laplacian on a bounded set inR n. The proof is based on a variational technique similar to that used by Weyl for the Laplacian. As an application of our estimates we prove stability in the maximum norm for the Crank-Nicolson method for the heat equation on a bounded set.

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Authors and Affiliations

  1. Department of Mathematics, Youngstown State University, 44503, Youngstown, Ohio, USA

    R. L. Burden & G. W. Hedstrom

  2. Department of Mathematics, Case Western Reserve University, 44106, Cleveland, Ohio, USA

    R. L. Burden & G. W. Hedstrom

Authors
  1. R. L. Burden
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  2. G. W. Hedstrom
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Additional information

The research of the second author was supported in part by National Science Foundation grant GP-30735X.

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Burden, R.L., Hedstrom, G.W. The distribution of the eigenvalues of the discrete Laplacian. BIT 12, 475–488 (1972). https://doi.org/10.1007/BF01932957

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  • DOI: https://doi.org/10.1007/BF01932957

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