|MadSci Network: Astronomy|
The first thing to remember is that you don't actually need a computer to answer this sort of thing - after all, the ancient Chinese for example used to be able to predict forthcoming eclipses. All the computer does is reduce the huge number of calculations needed and make them quicker.
More details can be found here
One other thing to look at is the Saros periods - each eclipse belongs to a Saros cycle which predicts the time until another eclipse. A good reference to start on this is here .
Try the links in the MadSci Library for more information on Astronomy.