Senu, N.; Suleiman, M.; Ismail, F.; Othman, M. A singly diagonally implicit Runge-Kutta-Nyström method for solving oscillatory problems. (English) Zbl 1229.65124 IAENG, Int. J. Appl. Math. 41, No. 2, 155-161 (2011). Summary: A singly diagonally implicit Runge-Kutta-Nyström method (RKN) is developed for second-order ordinary differential equations with periodical solutions. The method has algebraic order four and phase-lag order eight at a cost of four function evaluations per step. This new method is more accurate when compared with current methods of similar type for the numerical integration of second-order differential equations with periodic solutions, using constant step size. Cited in 5 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations Keywords:Runge-Kutta-Nyström method PDFBibTeX XMLCite \textit{N. Senu} et al., IAENG, Int. J. Appl. Math. 41, No. 2, 155--161 (2011; Zbl 1229.65124)