LCNO Sturm-Liouville problems: computational difficulties and examples

Summary.

In this paper we give a new proof of a theorem of Bailey, Everitt and Zettl on the convergence of truncated approximations to limit circle (LC) Sturm-Liouville problems, both non-oscillatory (LCNO) and oscillatory (LCO). The proof gives an error bound not previously available. We prove a theorem on the conditioning of LCNO problems with respect to non-Friedrichs boundary conditions. We present numerical experiments which illustrate how the theorem successfully predicts the conditioning of LCNO problems. Our work may also explain the performance of the code SLEIGN2 recently reported by Bailey et al. [1] on a number of problems.