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An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems. (English) Zbl 1264.65111
Summary: A procedure for the construction of an explicit optimized Runge-Kutta-Nyström method with four stages and of fifth algebraic order is provided. The variable coefficients of the preserved method result after nullifying the phase-lag, the dissipative error and the first derivative of the phase-lag. We can see the efficiency of the new method through its local truncation error. Furthermore, we compare the new method’s efficiency to other numerical methods. This is shown through the integration of the two-body problem with various eccentricities and of four other initial value problems.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L70Error bounds (numerical methods for ODE)
70F05Two-body problems
Full Text: DOI
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