LCNO Sturm-Liouville problems: Computational difficulties and examples (Q1347047)

Limit circle Sturm-Liouville non-oscillatory (LCNO) and oscillatory problems are discussed considering non-Friedrichs boundary conditions. Criteria are given by which inherently difficult limit circle (LC) problems may be distinguished from easy ones. The result of \textit{P. B. Bailey, W. N. Everitt} and \textit{A. Zettl} [Result. Math. 20, No. 1/2, 391-423 (1991; Zbl 0755.65082)] concerning interval truncation for LC problems is newly proved. By this proof an error bound is obtained. Conditioning of the non-Friedrichs eigenproblems is dealt with. Numerical examples including the Bessel equation and a problem with adjustable conditioning are analyzed. The regularizing transformation of \textit{H.-D. Niessen} and \textit{A. Zettl} [Proc. Lond. Math. Soc., III. Ser. 64, No. 3, 545-578 (1992; Zbl 0768.34015)] which may be used to convert an LCNO problem into a regular form, may still yield a problem which causes difficulties.