ChE 348 Homework # 5
_______________________________________________________________________
_
•
Finite Differences
1.
Suppose a car is traveling on a straight road.
Estimate (by hand) the speed of the car
when
t
= 0. 4, and 8 sec with O(
h
2
), using the following times and positions.
Time, sec
0
2
4
6
8
Distance, m
0
25
90
230
750
2.
Write a computer program to find derivative of exp(
x
) at
x
= 0.5 using
forward
and
backward
difference representations of O(
h
) and O(
h
2
) and
central
difference
representations of O(
h
2
)
and O(
h
4
).
Use stepsizes
h
=
0.1 and 0.05.
Compared the
results with each other and with exact answer.
(DO NOT USE BUILTIN MATLAB FUNCTIONS)
•
Gaussian Elimination
3.
Solve (by hand) the following linear systems using Gaussian elimination and two
digit rounding arithmetic, with partial pivoting if necessary.
Do not record the
equations.
(a) 4
x
1
+
x
2
+
2
x
3
= 9,
2
x
1
+
4
x
2
–
x
3
= –5,
x
1
+
x
2
–
3
x
3
= –9.
(b)
x
1
–
x
2
+
3
x
3
= 2,
3
x
1
–
3
x
2
+
x
3
= –1,
x
1
+
x
2
= 3.
4.
Write a Gaussian elimination code and use it to solve the following systems of linear
equations
Ax
=
b
(a)
A
=
8
7
7
7
6
7
6
6
5
5
6
5
4
4
4
5
,
b
=
29
25
21
17
The exact answer is
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 Spring '08
 Chelikowsky
 Gaussian Elimination, #, LU factorization, 8 Sec

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