Ciftci, Hakan; Hall, Richard L.; Saad, Nasser Asymptotic iteration method for eigenvalue problems. (English) Zbl 1070.34113 J. Phys. A, Math. Gen. 36, No. 47, 11807-11816 (2003). The main task of the present work is to introduce a new technique to solve second-order homogeneous linear differential equations \[ y''=\lambda_0(x)y'+s_0(x)y,\tag{*} \] where \(\lambda_0,s_0\in C_\infty(a,b)\). The following result is established:The differential equation (*) has the general solution \[ y(x)=\exp\left(-\int^x\alpha dt\right)\left[C_2+C_1\int^x\exp\left(\int^t(\lambda_0(\tau)+2\alpha(\tau))d\tau\right)dt\right] \] if for some \(n>0\) \[ \frac{s_n}{\lambda_n}=\frac{s_{n-1}}{\lambda_{n-1}}\equiv\alpha, \] where \(\lambda_k=\lambda'_{k-1}+s_{k-1}+\lambda_0\lambda_{k-1}\) and \(s_k=s'_{k-1}+s_0\lambda_{k-1}\) for \(k=1,2,...,n\).Applications to Schrödinger-type problems, including someones with highly singular potentials, are presented. Reviewer: Andrey Ivanovic Sedov (Magnitogorsk) Cited in 4 ReviewsCited in 87 Documents MSC: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators 34A30 Linear ordinary differential equations and systems 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis Keywords:iteration method; eigenvalue PDFBibTeX XMLCite \textit{H. Ciftci} et al., J. Phys. A, Math. Gen. 36, No. 47, 11807--11816 (2003; Zbl 1070.34113) Full Text: DOI arXiv