Solving differential equations numerically using Arduino
As @tyblu already noted, yes, it's possible.

Of course, it depends what you mean by "realtime", and how accurate results you want. Another possibility - depending on your system - may be offloading calculations to host computer (Arduino reads inputs, writes numbers to serial (or wirelessly with xbee, for example), computer calculates whatever you want to calculate and prints results to Arduino, and then Arduino decides what it'll do (change outputs)).