MATH 445
COMPUTER PROJECT 2
DUE WEDNESDAY, DECEMBER 2, 2009 AT THE LECTURE
You are free to use any programming language or environment and any help you want.
Please, use at least a 10pt font, and do not submit more than 12 pages of printouts for this
assignment.
Points can be taken off for using very small letters or producing too many pages
of output.
The objective of this assignment is to see how implicit numerical schemes work for parabolic and hyperbolic
equations.
Problem 1.
Consider the heat equation
u
t
(
x, t
) = 0
.
25
u
xx
(
x, t
)
,
0
< t
≤
2
,
0
< x <
1
,
with
u
(0
, t
) =
u
(1
, t
) = 0 and
u
(
x,
0) =
‰
20
x,
0
≤
x
≤
1
/
2
20(1

x
)
,
1
/
2
≤
x
≤
1
.
Solve it numerically by the CrankNicholson method taking
h
=
k
= 0
.
1.
Plot a 3D graph of the result.
Then
compare the result with the Fourier series solution (use your judgement as to how many terms to keep in the Fourier
series: this is your only chance to get to the exact solution as close as possible).
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 Fall '07
 Friedlander
 Math, Fourier Series, Partial differential equation, exact solution

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