Homework

Write a program to simulate the propagation of heat in a thin insulated rod, as discussed in this lesson. Your program should prompt the user for:

• the temperature of the left heat source,
• the temperature of the right heat source,
• the initial temperature of the rod,
• the number of segments (up to 20) into which the rod should be divided,
• the number of time units to simulate, and
• the value of the constant C.

You should assume that the rod is one unit long. Thus, if you divide the rod into N segments, each segment will be 1/N units long.

Recall that

Be sure to choose values of C so that s is between 0 and 1; anything else is physically impossible! You'll get the most interesting simulations if s is approximately 0.5.

Once your program has read in all of the initial conditions, it should first display the initial temperature of each segment of the rod, and then the temperature of each segment following each tick of simulated time. You will find a function for displaying temperature histograms in the file ``heat.c'' in your ``examples'' directory.