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Aim
Theory
Pretest
Procedure
Simulation
Posttest
References
Contributors
Feedback
ODE: Milne's Method
Choose difficulty:
Beginner
Intermediate
Advanced
The Milne's Method is a
a: direct method
Explanation
Explanation
b: indirect method
Explanation
Explanation
c: fixed point iterative method
Explanation
Explanation
d: predictor - corrector method
Explanation
Explanation
The predicted value given by Milne's Method
a:
y
p
=
h
f
(
x
0
,
y
0
)
y_p = hf(x_0, y_0)
y
p
=
h
f
(
x
0
,
y
0
)
Explanation
Explanation
b:
y
p
=
y
0
+
h
f
(
x
0
,
y
0
)
y_p = y_0 + hf(x_0, y_0)
y
p
=
y
0
+
h
f
(
x
0
,
y
0
)
Explanation
Explanation
c:
y
p
=
y
0
+
4
h
3
[
2
f
1
−
f
2
+
2
f
3
]
y_p = y_0 + \frac{4h}{3}[2f_1 - f_2 + 2f_3]
y
p
=
y
0
+
3
4
h
[
2
f
1
−
f
2
+
2
f
3
]
Explanation
Explanation
d:
y
p
=
y
3
+
h
24
[
55
f
3
−
59
f
2
+
37
f
1
−
9
f
0
]
y_p = y_3 + \frac{h}{24}[55f_3 - 59f_2 + 37f_1 - 9f_0]
y
p
=
y
3
+
24
h
[
55
f
3
−
59
f
2
+
37
f
1
−
9
f
0
]
Explanation
Explanation
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