Simos, T. E. A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. (English) Zbl 0990.65079 IMA J. Numer. Anal. 21, No. 4, 919-931 (2001). Summary: An exponentially-fitted Runge-Kutta method for the numerical integration of the radial Schrödinger equation is developed. Theoretical and numerical results obtained for the well known Woods-Saxon potential show the efficiency of the new method. Cited in 56 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34B05 Linear boundary value problems for ordinary differential equations Keywords:exponential fitting; Schrödinger equation; Runge-Kutta methods; bound-states problem; resonance problem; numerical results; Woods-Saxon potential Software:REDUCE PDFBibTeX XMLCite \textit{T. E. Simos}, IMA J. Numer. Anal. 21, No. 4, 919--931 (2001; Zbl 0990.65079) Full Text: DOI