An optimized Runge-Kutta method for the solution of orbital problems

Authors:
Z. A. Anastassi;T. E. Simos
Affiliations:
Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese GR-22 100 Tripolis, Greece;Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese GR-22 100 Tripolis, Greece
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Year:
2005

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Abstract

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.