The Iteration method for computing eigenvalues of non-definite Sturm-Liouville problem

In this paper, we consider the differential equation y +(ρr(x)-q(x))y=0 , (E) with Dirichlet boundary condition (i.e., y(0)=y(1)=0), ρ is a real parameter and the function r(x)=x which has a zero, the so-called turning point. From the numerical viewpoint not enough studies have been done on eigenvalues of non-definite Sturm-Liouville problems(SLP). So iterative method is investigated for approximation of eigenvalues of Sturm-Liouville. The numerical examples show the asymptotic estimates for the eigenvalues of (E) are in agreement with our results and encouraging.