The principal investigators study the approximation of the spectrum of singular self-adjoint Sturm-Liouville problems by regular Sturm-Liouville problems. They focus efforts on the conjecture that any point in the spectrum of a singular problem is the limit of a sequence of eigenvalues of a family of regular problems, and on its computational consequences. A major part of the effort is devoted to development of SLEIGN2, a successor to the SLEIGN code for computing eigenvalues of Sturm-Liouville problems. Sturm-Liouville problems arise in transport theory, quantum physics, quantum chemistry, geophysics, and acoustics. Computation of their solutions is important. Where the problem is regular, several software codes are available to help calculate solutions. This project undertakes to create software for singular problems.
