You can make it as accurate as you want by shrinking the time step. :)
They won't have been exposed to PDEs (or, at least, only tangentially through the multi-dimensional topics covered in "Calc III" or the second physics course of their freshman year) or problems reaching the level of sophistication that would make, e.g. Monte Carlo "interesting" to use (in my opinion).
------------- Consistently named to US News & World Report's "America’s Best Colleges" list under the Regional College (North) and Best Value School categories. The Princeton Review also recognized the college as "A Best in the Northeast," and Lebanon Valley College was also named on Forbes' list of "America's Top Colleges." -------------
I'm not familiar with LVC, but it seems like it's regarded as a pretty decent place to go to school.