Accurate Estimations of Any Eigenpairs of <i>N</i>-th Order Linear Boundary Value Problems

Abstract

This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n-th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on the selection of a particular type of cone for each eigenpair to be determined, the recursive application of the operator associated to the equivalent integral problem to functions belonging to such a cone, and the calculation of the Collatz–Wielandt numbers of the resulting functions.

Keywords

• <i>n</i>-th order linear differential equation
• two-point boundary value problem
• sign-regular kernel
• eigenvalue
• eigenfunction
• Collatz–Wielandt numbers