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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
9-18 Mathematical Methods
found by a corrector formula, which we derive by
Newton’s backward interpolation formula at f
1
as
2
11 1
2
1
(1)
(, )
2
(1)(2)
6
nn
fxy f nf f
nn n
f
+
=+∇+
++
+∇+
(9.52)
Hence
+
=+ +∇+
++
+∇+
1
0
22
10 1 1 1
3
1
(1)
2
(1)(2)
6
x
x
nn
yy fnf f
nn n
fdx
(9.53)
Putting x = x
1
+ nh, dx = h dn and neglecting
fourth and higher-order differences and replacing
the differences by the functional values, we obtain
10 1 0 12
(9 19 5 )
24
h
yy f f ff
−−
=+ +
(9.54)
which is called the Adams–Moulton corrector
formula. Then an improved value of f
1
is calculated
and again the corrector (9.54) is applied to find a
still better value y
1
. This step is repeated ...
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Publisher Resources

ISBN: 9781299446557Publisher Website