The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra

ABSTRACT

The software package SLEDGE has as one of its options the estimation of spectral density functions p(t) for a wide class of singular Strurm-Liouville problems. In this article the underlaying theory and implementation issues are discussed. Several examples exhibiting quite varied asymptotic behavior in p are presented.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Boundary value problems

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Eigenvalues and eigenvectors (direct and iterative methods)
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

General Terms:
Algorithms, Performance

Keywords:
Strum-Liouville problems, continuous spectrum, eigenfunction norm, eigenvalue, limit circle, limit point, oscillatory, singular endpoints, spectral density functions