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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
8-16 Mathematical Methods
(i) Trapezoidal Rule
0 1234567 8
[2( )]
2
1
[1.0 2(2.7649 2.0381) 0.5] 0.6941
16
h
I
yyyyyyyyy=++++++++
=+ + +=
(ii) Simpson’s Rule
08 1357
2468
[4( )
3
2( )]
1
[1.0 4(2.7649) 2(2.0381)]
24
0.693158333 0.6932
h
Iyyyyyy
yyyy
=+++++
++++
=+ +
=
The exact value of I =lo
g
e
2 = 0.693147…. The
value obtained by Simpson’s rule is close to this.
Hence Simpson’s rule gives a better approximation
than the Trapezoidal rule.
Example 8.18
Evaluate
1
0
(1 sin 4 )
x
exdx
+
with equally spaced
quadrature nodes x
0
, x
1
, x
2
, x
3
and x
4
separated
by distance
=
1
4
h
using (i) Trapezoidal rule,
(ii) Simpson’s and (iii) Boole’s rules.
Solution Constructing the table of ...
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Publisher Resources

ISBN: 9781299446557Publisher Website