Numerical methods for approximating eigenvalues of boundary value problems

Abstract

This paper describes some new finite difference methods for the approximation of eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation of the type (py″)′​′−(qy′)′+(r−λs)y=0. The smallest positive eigenvalue of some typical eigensystems is computed to demonstrate the practical usefulness of the numerical techniques developed.