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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
9-8 Mathematical Methods
and , using the following abbreviations:
1
2
2
23
3
2
33
xy
xx xy yy
xxx xxy xyy yyy
Ff ff
Ff ff ff
Ff ff ff ff
=+
=+ +
=+ +
(9.27)
w
e can write (9.25) as
23
2
1221
4
2
322 2121
()
26
(3)
24
hh
yhf f F F fF
h
FfF fFfF
Δ= + + +
=++++
(9.28)
An RK for
mula of order
n
is a for
mula which
expresses Δy in terms of n values of the function
f (x, y) in such a manner that the value obtained
coincides with equation (9.28) as far as the terms
involving h
n
are concerned.
Now we express Δy in the form
Δy = ak
1
+ bk
2
+ ck
3
+ dk
4
(9.29)
where
[]
1
21
22 33
123
32
2
2
1221
3
32 2
322 21
43
2
2
1221
3
32
3
(, )
(, )
66
(, )
(2)
2
(36)
6
,
(2)
2
(3
6
khfxyhf
khfxmhymk
mh mh
hf mhF F
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Publisher Resources

ISBN: 9781299446557Publisher Website