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
DOI:
https://doi.org/10.1090/S0025-5718-1971-0301955-6
MathSciNet review:
0301955
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Abstract | References | Similar Articles | Additional Information
Abstract: The fixed membrane problem $\Delta u + \lambda u = 0$ in $\Omega ,u = 0$ on $\partial \Omega$, for a bounded region $\Omega$ 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, $O({h^4})$ 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 $\Delta u + qu = f$ in $\Omega ,u = 0$ in $\partial \Omega$, is also given.
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Additional Information
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