Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem

Abstract

This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py″)′​′+(q−λr)y=0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.

Keywords

• band-matrices
• finite-difference methods
• generalized eigenvalue problem
• positive definite matrices
• two-point boundary value problems.