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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 341
/
Section A
/
5
/
d
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Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 341
Section A
5
2026-09-28
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Solution
d
Solution
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d
The composition is palindromic, and hence
G
α
(
−
t
)
=
F
(
−
α
t
)
F
(
−
(
1
−
2
α
)
t
)
F
(
−
α
t
)
=
G
α
(
t
)
−
1
.
(1)
Thus
G
α
is symmetric. Part
c
cancels the cubic term in its odd
formal logarithm
;
symmetry
forbids
a
fourth-degree term, so the next possible defect has degree five. Therefore
G
α
(
t
)
=
e
t
(
A
+
B
)
+
O
(
t
5
)
,
(2)
which makes the composition
a
fourth-order method.
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(11)
5
Section A
Paper 341
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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