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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:

- As a function of the radius of the brat, when is it done?
- As a function of heat of the grill, when is it done?
- As a function of the initial temperature of the brat, when is
it done?
- As a function of the water content in the brat, when is
it done?
- Does it matter how fast we spin the thing on the grill?
- Does it matter how close together we put these things on the grill?
- Does it matter what the temperature in the room is?
- Etc., etc., etc.