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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
8-2 Mathematical Methods
8.1.3 Numerical Differentiation
by Newton’s Backward
Interpolation Formula
Differentiating with respect to x Newton’s Backward
Interpolation Formula
2
0
3
(1)
()
2!
(1)(2)
3!
nn
n
pp
yx y p y y
pp p
y
+
=+∇+
++
+∇+
we obtain
2
2
3
11
() (2 1)
2
362
6
nn
n
yx y p y
h
pp
y
=∇+ +∇
++
+∇+
(8.9)
23
2
2
4
1
() ( 1)
61811
12
nn
n
yx y p y
h
pp
y
=∇++∇
′′
++
+∇
(8.10)
Special Case
When x = x
n
, p = 0 and we have
234
1111
()
234
nnnnn
yx y y y y
h
⎡⎤
=∇+∇+∇+∇+
⎢⎥
⎣⎦
(8.11)
23 4
2
111
()
12
nnnn
yx y y y
h
⎡⎤
=∇+∇+∇
′′
⎢⎥
⎣⎦
(8.12)
8.1.4 Numerical Differentiation
by Stirling’s Formula
Differentiating Stirling’s formula
2
2
01
01
33
2
12
22
4
2
()
1! 2 2!
(1)
3! 2
(1)
4
yy
pp
yx y y
yy
pp
pp
y
−−
Δ+Δ
⎛⎞
=+ +
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Publisher Resources

ISBN: 9781299446557Publisher Website