Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 2, Pages 183-192

High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon

Philip W. Sharp

Department of Mathematics, University of Auckland, Auckland Private Bag 92019, New Zealand

Copyright © 2000 Philip W. Sharp. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Numerically integrated ephemerides of the Solar System and the Moon require very accurate integrations of systems of second order ordinary differential equations. We present a new family of 8-9 explicit Runge-Kutta pairs and assess the performance of two new 8-9 pairs on the equations used to create the ephemeris DE102. Part of this work is the introduction of these equations as a test problem for integrators of initial value ordinary differential equations.