Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N25

Retrieve articles in all journals with MSC: 65N25

Additional Information

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia