Sturm-Liouville eigenvalue problems arise naturally when separation of variables, variational methods, or other considerations are used to solve technical problems in engineering, physics, biology, and the social sciences. Explicit (closed form) evaluation of eigenvalues and eigenfunctions is rarely possible. In this seminar talk, I will present joint work with Ron Guenther on shooting methods for the accurate approximation of eigenvalues and eigenfunctions of both regular and singular Sturm-Liouville problems. Two attributes of the methods are: (1) they are natural and (2) any particular eigenvalue, eigenfunction pair is determined independently of any other pair, so there is no accumulation of round-off errors when several pairs are determined.
Several tables and graphs generated by the shooting methods will be discussed.