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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:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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