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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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: 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

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0301955-6
PII: S 0025-5718(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