Numerical solution of the sturm liouville problem with periodic boundary conditions

Abstract

A recursive algorithm for the implicit derivation of the characteristic equation of a symmetric general tridiagonal matrix of order n is derived from a finite difference discretisation of a periodic Sturm Liouville problem. The algorithm yields a Sturmian sequence of polynomials from which the eigenvalues can be obtained by the use of the well known standard bisection process. An extension to Wilkinson's method for deriving the eigenvectors of symmetric tridiagonal matrices yields the required eigenvectors of the periodic Sturm Liouville problem.