A fourth-order finite-difference approximation for the fixed membrane eigenproblem

Author:
J. R. Kuttler

Journal:
Math. Comp. **25** (1971), 237-256

MSC:
Primary 65N25

MathSciNet review:
0301955

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Abstract | References | Similar Articles | Additional Information

Abstract: The fixed membrane problem in on , for a bounded region of the plane, is approximated by a finite-difference scheme whose matrix is monotone. By an extension of previous methods for schemes with matrices of positive type, convergence is shown for the approximating eigenvalues and eigenfunctions, where *h* is the mesh width. An application to an approximation of the forced vibration problem in in , is also given.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1971-0301955-6

Keywords:
Finite-differences,
membrane,
fixed membrane,
eigenvalues,
elliptic partial differential equations,
monotone matrices,
forced vibration problem,
discrete Green's function

Article copyright:
© Copyright 1971
American Mathematical Society