In the current volume, we continue the dialogue that we started in the previous volume, where Alice and Bob developed a gravitational 2-body code, based on the simplest of all integration algorithms, the forward Euler method. They are now ready to implement a variety of other algorithms, such as the leapfrog and Runge-Kutta schemes, as well as multi-step methods. They will even succeed in implementing two different eigth-order schemes.

Besides thanking our home institutes, the Institute for Advanced Study in Princeton and the University of Tokyo, we want to convey our special gratitude to the Yukawa Institute of Theoretical Physics in Kyoto, where we have produced a substantial part of our ACS material, including its basic infrastructure, during extended visits made possible by the kind invitations to both of us by Professor Masao Ninomiya. In addition, we thank the Observatory of Strasbourg, where the kind invitation of Professor Christian Boily allowed us to make a rapid beginning with the current volume.

It is our pleasure to thank Steve Giess, Douglas Heggie, Stephan Kolassa, Ernest Mamikonyan and Michele Trenti for their comments on the manuscript.

Piet Hut and Jun Makino

Kyoto, July 2004

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