
Consider the onedimensional heat equation with k = 1, N
= 20, and a random initial temperature distribution
generated by
u[i] = rand()/(double)RAND_MAX;
Find and graph the temperature distribution for t = 1 ..
10. Use this as a basis for understanding the longterm
behavior of the temperature distribution. If necessary
compute it for larger values of t. Comment on any
phenomena which seem of interest.

Repeat the analysis of the previous problem for the
twodimensional heat equation with N = 11 and a random
initial temperature distribution given by
u[i,j] = rand()/(double)RAND_MAX;

Note: For some reason our beloved compiler does
not seem to know about RAND_MAX any more. It should be
defined in <stdlib.h> (see p. 252 of "The C
Programming Language" by Kernighan and Richie,
second edition). A temporary fix for this is to put the
line
#define RAND_MAX 100000000
in your program. You can use a different value or
RAND_MAX if you like. The point is to use a large
integer.