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Past exam of the mathematics course of the University of Cambridge
/
2019
/
ia
/
Paper 2
/
5C
/
a
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2019
ia
Paper 2
5C
a
Created
2026-09-24
Updated
2026-09-29
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The
Taylor expansions
about
t
n
are
y
n
±
1
=
y
n
±
h
y
n
′
+
2
h
2
y
n
′′
±
6
h
3
y
n
′′′
+
24
h
4
y
n
(
4
)
+
O
(
h
5
)
.
(1)
Adding them cancels the
odd
powers
of
h
and gives
h
2
y
n
+
1
−
2
y
n
+
y
n
−
1
=
y
′′
(
t
n
)
+
12
h
2
y
(
4
)
(
t
n
)
+
O
(
h
4
)
.
(2)
Thus the
centred finite difference
has
truncation error
O
(
h
2
)
, so
α
=
2
.
Ancestors
(11)
a
5C
Paper 2
ia
2019
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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