Accurate approximation of eigenvalues and zeros of selected eigenfunctions of regular Sturm-Liouville problems

Abstract

A method for simultaneously approximating to high accuracy the corresponding eigenvalue and zeros of the ( n + 1 ) (n + 1) st eigenfunction of a regular Sturm-Liouville eigenvalue problem is presented. It is based upon equilibrating the minimum eigenvalues of several problems on subintervals that form a partition of the orginal interval. The method is easily derived from classical mini-max variational principles. The equilibration is accomplished iteratively using an approximate Newton Method. Numerical results are given.