A test package for Sturm-Liouville solvers

ABSTRACT

The author and colleagues have produced a collection of 60 test problems which offer a realistic performance test of the currently available automatic codes for eigenvalues of the classical Sturm-Liouville problem. We describe a Fortran implementation and the considerations that went into its design. A novel feature is that (almost) all the code defining one problem is textually contiguous in the Fortran text, unlike for example the DETEST package for ODE initial-value solvers where the definition of a problem is spread over several routines. The described implementation forms the infrastructure of the SLDRVER interactive package which supports exploration of a set of Sturm-Liouville problems with the four SL-solvers SLEIGN, SLEDGE, SL02F, and SLEIGN2. A “standard” set of 60 problems is provided, but it is simple to replace this by another one.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

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

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE

General Terms:
Algorithms, Measurement, Performance

Keywords:
Sturm-Liouville problem, test-problem collection, testing software