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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Numerical Differentiation and Integration 8-11
If we replace
41
140
in the last term by
3
10
, the error
made will be
−=
3
41 1
10 140 140
0.007
which is neg-
ligib
le w
hen
h
and Δ
6
y
0
are small.
Substituting for Δy
0
, Δ
2
y
0
, … and simplifying,
we obtain
6
0
0123456
3
[5 6 5 ]
10
x
x
h
I y dx y y y y y y y==++++++
(8.47)
(Here the curve is approximated by a sixth-degree
polynomial curve and n must be a multiple of 6,
n = 6m.)
Total error
=−
=
6(6)
(6) (6) (6)
(6)
01 1
()
();
140
() max( , , )
n
ba
hy
yyyy
ξ
ξ
(8.48)
Example 8.7
Evaluate
∫∫
44 4
23 4
00 0
(a) (b) (c) x dx x dx x dx
by
(i) Trapezoidal rule and (ii)
Simpson’s rule.
Solution Writing the table of values
where X =
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Publisher Resources

ISBN: 9781299446557Publisher Website