Kalogiratou, Z.; Simos, T. E. Construction of trigonometrically and exponentially fitted Runge–Kutta–Nyström methods for the numerical solution of the Schrödinger equation and related problems – a method of 8th algebraic order. (English) Zbl 1002.65077 J. Math. Chem. 31, No. 2, 211-232 (2002). An \(m\)-stage Runge-Kutta-Nyström method for the investigation of ordinary differential equations of the form \[ u''(t)= f(t,u(t)), \] for which it is known that their solution is periodic or oscillating, is presented. Special attention to the numerical solution of the Schrödinger equation is given. Reviewer: Laura-Iulia Aniţa (Iaşi) Cited in 81 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34C25 Periodic solutions to ordinary differential equations 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:trigonometrically-fitted; exponentially-fitted; Runge-Kutta-Nyström method; Schrödinger equation; scattering problems; resonance problem; periodic solutions; oscillating solutions PDFBibTeX XMLCite \textit{Z. Kalogiratou} and \textit{T. E. Simos}, J. Math. Chem. 31, No. 2, 211--232 (2002; Zbl 1002.65077) Full Text: DOI