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ChE 348 Homework # 10
___________________________________________Due: Thursday, 18 November 2010
1.
Solve (
by hand
) the following problems using Euler’s method with a stepsize of
h
=
0.1.
Compute the error using the true answer Y(
x
).
(a)
[]
)
arctan(
)
(
0
)
0
(
,
5
.
0
0
,
))
(
cos(
)
(
2
/
x
x
Y
Y
x
x
Y
x
Y
=
=
≤
≤
=
(b)
[]
2
2
2
/
1
)
(
0
)
0
(
,
5
.
0
0
,
)
(
2
1
1
)
(
x
x
x
Y
Y
x
x
Y
x
x
Y
+
=
=
≤
≤
−
+
=
2.
Using the approximation
h
x
y
x
y
x
y
x
y
n
n
n
n
2
)
(
3
)
(
4
)
(
)
(
'
1
1
1
−
+
−
−
+
−
≈
derive the following numerical method for solving initial value problems.
)
,
(
2
3
4
1
1
1
1
−
−
−
+
−
−
=
n
n
n
n
n
y
x
hf
y
y
y
3.
Use the trapezoidal rule predictorcorrector with
h
= 0.1 to compute (
by hand
)
approximate value of
y
(0.3) for the following initial value problems.
()
()
2
2
2
1
)
(
:
0
)
0
(
,
0
2
1
1
'
x
x
x
y
solution
true
y
y
x
y
+
=
=
=
+
+
−
4.
Derive the numerical method based on using Simpson’s rule to approximate the
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This note was uploaded on 11/28/2010 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Chelikowsky

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