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"The Way the Ball Bounces," by Brian Hayes. American Scientist, July-August 1996, pages 331-335.
When two smoothly rolling billiard balls collide on a table, the outcome seems intuitively pretty obvious---they knock against each other and then roll their separate ways. But how does one produce a reliable computer simulation of such an event? This article explores various approaches to this question, showing how some of the naive ideas that first come to mind have computational idiosyncrasies that do not parallel anything that happens on the billiard table. Coming up with a simulation that mimics what is happening physically is surprisingly difficult to do. Exploring this simple example, the article reveals a great deal about the difficulties of coming up with good computer simulations and the importance of knowing their limitations.