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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.

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
65L70 Error bounds for numerical methods for ordinary differential equations
70M20 Orbital mechanics
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