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Zbl 1063.65059
Anastassi, Z.A.; Simos, T.E.
An optimized Runge-Kutta method for the solution of orbital problems. (English)
[J] J. Comput. Appl. Math. 175, No. 1, 1-9 (2005). ISSN 0377-0427

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 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L70 Error bounds (numerical methods for ODE)
70M20 Orbital mechanics

Keywords: dispersion; dissipation; error bounds; explicit Runge-Kutta methods; numerical results; periodic orbital problems

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Zentralblatt MATH Berlin [Germany]