Numerical Analysis –MTH603 VU
© Copyright Virtual University of Pakistan 1
D
DI
IF
FF
FE
ER
RE
EN
NT
TI
IA
AT
TI
IO
ON
N
U
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SI
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FF
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RE
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AT
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S:
:
A
Ap
pp
pl
li
ic
ca
at
ti
io
on
ns
s:
:
R
Re
em
me
em
mb
be
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U
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si
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g
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if
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er
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en
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e
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e
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ba
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if
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er
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ta
ai
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ne
ed
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t
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f
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ol
ll
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rm
mu
ul
la
ae
e:
:
234
000
00 0
1
234
yyy
Dy y y
h
∆∆∆
′
==∆− + − +
"
23
200
20
00
22
45
00
111 5
12 6
yy
dy
Dy y
dx h yy
∆−∆
′′
===
+∆ −∆ +
"
234
1
234
nnn
nnn n
yyy
dyDyy y
dx h
∇∇∇
′
===∇− + + +
"
(
22345
2
1115
12 6
nn nn n n
yDy y y y y
h
′′ = = ∇+∇+∇+∇+
"
2246
2
111
12 90
yDy y y y
h
δδδ
′′ == − + −
"
35
11 3
24 640
dyy Dy y y y
dx h
δδ δ
′
== = − + −
"
R
Re
ec
ca
al
ll
l
f
fr
ro
om
m
w
wh
ha
at
t
w
we
e
m
me
en
nt
ti
io
on
ne
ed
d
i
in
n
t
th
he
e
l
la
as
st
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l
le
ec
ct
tu
ur
re
e
t
th
ha
at
t
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or
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lc
cu
ul
la
at
ti
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ng
g
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he
e
s
se
ec
co
on
nd
d
d
de
er
ri
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va
at
ti
iv
ve
e
a
at
t
a
an
n
i
in
nt
te
er
ri
io
or
r
t
ta
ab
bu
ul
la
ar
r
p
po
oi
in
nt
t,
,
w
we
e
u
us
se
e
t
th
he
e
e
eq
qu
ua
at
ti
io
on
n
2246
2
113
12 90
Dh
δδδ
=−+−
"
W
Wh
hi
il
le
e
f
fo
or
r
c
co
om
mp
pu
ut
ti
in
ng
g
t
th
he
e
f
fi
ir
rs
st
t
d
de
er
ri
iv
va
at
ti
iv
ve
e
a
at
t
a
an
n
i
in
nt
te
er
ri
io
or
r
t
ta
ab
bu
ul
la
ar
r
p
po
oi
in
nt
t,
,
w
we
e
i
in
n
g
ge
en
ne
er
ra
al
l
u
us
se
e
a
an
no
ot
th
he
er
r
c
co
on
nv
ve
en
ni
ie
en
nt
t
f
fo
or
rm
m
f
fo
or
r
D
D,
,
w
wh
hi
ic
ch
h
i
is
s
d
de
er
ri
iv
ve
ed
d
a
as
s
f
fo
ol
ll
lo
ow
ws
s.
.
M
Mu
ul
lt
ti
ip
pl
ly
y
t
th
he
e
r
ri
ig
gh
ht
t
h
ha
an
nd
d
s
si
id
de
e
o
of
f
35
11 3
24 640
dyy Dy y y y
dx h
δδ δ
′
== = − + −
"
By 2
1( 4)
µ
δ
+
W
Wh
hi
ic
ch
h
i
is
s
u
un
ni
it
ty
y
a
an
nd
d
n
no
ot
ti
in
ng
g
t
th
he
e
B
Bi
in
no
om
mi
ia
al
l
e
ex
xp
pa
an
ns
si
io
on
n
12
2246
11315
11
4 8 128 48 64
δδδδ
−
+=−+− +
×
"
We get
24 35
13 1 3
18 128 24 640
Dh
µδδ δδδ
=−+ − − + −
""
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