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An optimized Runge-Kutta method for the solution of orbital problems. (English) Zbl 1063.65059
Summary: We present a new explicit Runge-Kutta method with algebraic order four, minimum error of the fifth algebraic order (the limit of the error is zero, when the step-size tends to zero), infinite order of dispersion and eighth order of dissipation. The efficiency of the newly constructed method is shown through the numerical results of a wide range of methods when these are applied to well-known periodic orbital 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)
70M20Orbital mechanics (general mechanics)
Full Text: DOI
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