CS 3414 Problem Statement 5

Probably the most common type of problem solved by computational scientists is a system of partial differential equations. PDEs are the basis of mathematical models in virtually all branches of science and engineering. Efficient and accurate numerical methods for approximately solving PDEs are of critical importance; developing such methods is a very active area of ongoing research. This problem is a very simple example of this kind of activity.

Suppose you have been hired as a (very expensive) consultant by ``Bill's Brats.'' In case you don't know, a bratwurst (pronounced ``brahtwurst'', unless you are from Chicago), is a fine pork-based sausage-like thing prized by natives of the Midwest and Germany. Bill owns a chain of bratwurst stands scattered around minor league baseball stadiums in Wisconsin and Illinois. Bill is a big believer in using sophisticated numerical methods to help improve his business. He has hired you to answer an important question:

How long do we really need to cook these things?

Bill has the idea that they could improve sales if they could just cook these bratwurst more quickly. He says there ought to be a way to figure out when a brat is done using numerical methods! He wants you to develop a numerical simulation that will allow him to answer questions like: