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Zbl 1082.65071
Franco, J.M.
A class of explicit two-step hybrid methods for second-order IVPs. (English)
[J] J. Comput. Appl. Math. 187, No. 1, 41-57 (2006). ISSN 0377-0427

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 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: numerical integration; two-step methods; explicit hybrid methods; second-order IVPs; comparison of methods; second-order initial value problems; Runge-Kutta-Nyström methods; numerical experiment

Cited in: Zbl 1136.65068

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