Correctness of Dorodnitsyn's method for approximate calculation of eigenvalues in a class of boundary value problems (Q1874919)

The authors prove the convergence of a method of \textit{A. A. Dorodnitsyn} [Uspechi. Mat. Nauk 7, 3--96 (1952; Zbl 0048.32402)] for numerical computation of the eigenvalues of the Sturm-Liouville problem \(y'' +(\lambda r+q)y=0\), with separated boundary conditions on \([0,\ell ]\), where \(r(x)=r_1 (x)x^{\alpha}\), \(\alpha >-1\), and \(r_1\) is continuous and positive, and \(q\) continuous and real-valued.