On the correction of finite difference eigenvalue approximations for sturm-liouville problems with general boundary conditions

Abstract

When finite difference and finite element methods are used to approximate continuous (differential) eigenvalue problems, the resulting algebraic eigenvalues only yield accurate estimates for the fundamental and first few harmonics. One way around this difficulty would be to estimate the error between the differential and algebraic eigenvalues by some independent procedure and then use it to correct the algebraic eigenvalues. Such an estimate has been derived by Paine, de Hoog and Anderssen for the Liouville normal form with Dirichlet boundary conditions. In this paper, we extend their result to the Liouville normal form with general boundary conditions.