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Computing the indices of Sturm–Liouville eigenvalues for coupled boundary conditions (the EIGENIND-SLP codes)

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
220
Identifiers
DOI: 10.1016/j.cam.2007.09.008
Keywords
  • Self-Adjoint Sturm–Liouville Problems
  • Indices Of Eigenvalues
  • Coupled Boundary Conditions
  • Prüfer Angle
  • Numerical Computations
Disciplines
  • Computer Science

Abstract

Abstract The main purpose of the EIGENIND-SLP codes is to compute the indices of known eigenvalues of self-adjoint Sturm–Liouville problems with coupled boundary conditions (BCs). The spectrum of the problems can be unbounded from both below and above. Using some recent theoretical results, the computation is converted to that of the indices of the same eigenvalues for appropriate separated BCs, and is then carried out in terms of the Prüfer angle. The algorithm so generated and its implementation are discussed, and numerous examples are presented to illustrate the theoretical results and various aspects of the implementation.

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