Upper and lower bounds for eigenvalues by finite difference methods

Abstract

A finite difference method is presented which gives a lower bound for the lowest eigenvalue of the membrane problem for any plane domain. Under certain assumptions on the domain one finds both upper and lower bounds for this eigenvalue by solving a single finite difference problem. The difference between the bounds can be estimated a priori and made arbitrarily small by choosing the mesh size sufficiently small.

Identifiers

DOI

10.1002/cpa.3160090329

Citations and references