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Past exam of the mathematics course of the University of Cambridge
/
2025
/
ib
/
Paper 2
/
17A
/
a
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2025
ib
Paper 2
17A
a
Created
2026-09-24
Updated
2026-09-25
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Write the internal stage
as
k
2
=
f
(
y
n
+
h
[(
1
−
θ
)
k
1
+
θ
k
2
])
.
(1)
The two methods have
θ
=
1/2
and
3/4
. Expansion gives stability
function
R
θ
(
z
)
=
1
−
θ
z
1
+
(
1
−
θ
)
z
+
(
1/2
−
θ
)
z
2
=
1
+
z
+
2
z
2
+
2
θ
z
3
+
O
(
z
4
)
.
(2)
Both therefore have order two; order three would require
θ
=
1/3
.
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a
17A
Paper 2
ib
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
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