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

摘要

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.