Error Analysis in the Approximation of Sturm]Liouville Spectral Density Functions

As one of its options the software package SLEDGE estimates Sturm]Liouville spectral density functions for problems having continuous spectrum. This paper contains the error analysis underlying SLEDGE’s approximations: error bounds, Richardson’s extrapolation, and stability analysis. Several alternate interpolation schemes are introduced and analyzed. An improvement to SLEDGE is suggested and tested.