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Consider the one-dimensional 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 long-term
behavior of the temperature distribution. If necessary
compute it for larger values of t. Comment on any
phenomena which seem of interest.
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Repeat the analysis of the previous problem for the
two-dimensional heat equation with N = 11 and a random
initial temperature distribution given by
u[i,j] = rand()/(double)RAND_MAX;
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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.