THE RECURSIVE METHOD FOR COMPUTING EIGENVALUES OF NON-DEFINITE STURM-LIOUVILLE PROBLEM

In this paper, we investigate the differential equationy′′+ (λr(x)-q(x))y=0, α≤x≤b; (E)with Dirichlet boundary condition (i.e., y(a) = y(b) = 0), y(b)=0), λ is a realparameter and the weight function r(x) = x which has a zero, the so-calledturning point. From the numerical viewpoint not enough studies havebeen done on eigenvalues of non-de nite Sturm-Liouville problems(SLP).So iteration method is investigated for approximation of eigenvalues ofSturm-Liouville. The numerical examples show the asymptotic estimatesfor the eigenvalues of (E) in [6] are in agreement with our results andencouraging.

Keywords:

Turning point , Sturm-Liouville , Recursive , Eigenvalues