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A class of explicit two-step hybrid methods for second-order IVPs. (English) Zbl 1082.65071
Summary: A class of explicit two-step hybrid methods for the numerical solution of second-order initial value problems (IVPs) is presented. These methods require a reduced number of stages per step in comparison with other hybrid methods proposed in the scientific literature. New explicit hybrid methods which reach up to order five and six with only three and four stages per step, respectively, and which have optimized the error constants, are constructed. The numerical experiments carried out show the efficiency of our explicit hybrid methods when they are compared with classical Runge-Kutta-Nyström methods and other explicit hybrid codes proposed in the scientific literature.

MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general