An Iterative Method for the Solution of Eigenvalue Problems

Abstract

A simple iterative procedure is developed for the determination of eigenvalues and eigenfunctions associated with the solution of Sturm-Liouville problems in a finite interval. Both the frequency and the displacement for a given mode may be determined with an accuracy which is independent of the accuracy involved in the calculation of other modes. Convergence of the iteration process is rapid, and the successive approximations to a given eigenvalue are shown to form a monotone sequence. The method is particularly useful when the coefficients of the differential equation are not expressed in analytical form.