.
dift l
'
⑥
Axab
Banded matrix
ncemerical
eq
system
of
eqs
alqebra
s
metlrod
.
.
Cordinary dieele eq )
ODE
-
,강
N
… 55가정구
한로그
ㅿ
d루
-
2
dx
2
-
a f
Introduce
=
.
Q cx )
.
discrete set of
points xj
_
a
.
j
=
0. 1
.
2
-
.
,
N
grid points
FiondTox )
5
on
TJ
FDM clinitedifference
method )
Taylon series expansion
h
5
hy
=
=
⑦
ajte j
h2
=
. -
=
:
arid spacing
h . uniform auid ←
spacing
.
TCx H 7
[(
5
=
Tag
)
h×
+
l5
놓hd
+
1,+ * d15
β d
리,
h4
4
+→
←
TCx )
+
πx H )
5
,
Tcx
-
5
.
)
-
n
=
-
2
=
h!5
×
+
a
a
t
* h ×기
' d
+
-
…
더 xsoTaerox
=
;
e
하이
끔
⑤ ×
ㅿ하
다5
=
t
(
π
)-
.
leadingento
FDM
Second- order FDM
슬이다
없니,
=
e
"
'
대,⑤+ '
first ordev FDM
-
' !+5⑤ +
× l.
=
c ;
-
…
…
hd
Tcn5
Tπ 5n ) +
l
→
)
2 T5 +
=
]
h
지
5
+
금b4
4!
-
-
+
) ⑤
leading
없다
n
π5
=
2엄
,
급
-
error
second orderFDs
-
ssubstitute thrs tormula to dife e eq
OCa)
'
{
Tje 2555 -3
n
j
→
-
o
Tw
ㆁ
=
s
J
=
θ⑮
j
=
.
boundang conditins
System of algebrarc qs .
.
1 2, ., N
tenm
→
-
( 2 tka
51 -
$
s
To = 0
TN
@ 5=
=
t
⑥ 5= 2 ,
①
*
n1
,
S
,
5
+
5
.
£
,
Ʃ
-
[3
e
π
-
C
J T25 T
.
) Fv- ++ -
Gs
=
1
.
2
,
.
Ny
O
"
.
W
j
hQ
+⑥=Q
thzar ,9 .
c2
-
4
=
.
=pQ 2
2
=QN
에
J
다
.
했
]
[.
JI
아마
.
"
임
.
…
f
-
다
.
onlyreele
dragonal
fleuents
mantses of
arond
.
banded
the main
h -m
∞
I
eqs
trou
Tri
-
diagonal
matrix
:
ai
B Cai bi ce ]
,
,
bo
=
[ ‰ . ]]GX
..
natrie
arerse
.
0
o .
.
⑥
Cpartial diele eq )
PDE
쭉
쫄
∞
oy "
+
ox
5
=
oy ;
xite π
=
=
Yjy y;
-
=
h
=
h
aniform
1
-
25222 )
(
1
=.
? 다없다
..
JIII
다.
.
) gnid spacings
…
.
2nd
-
order FDM
.
n5
+
~
2
=
2
4
TEeJ
s
⑥ =t5 =
1:
⑥ i= 2 5t : [3.
@ E
t
.
5
=
3
1
-
4
:
2Ti
⑤
: 5 fπ 51
E .+
그
a
. p+
Ti
0
-
j+5
∅
→
⑳
2
hQip
⑭
2
T3.0 .
3
+T
3. 2
2.
l4
O OO
4
.
.
θ ㅇ
.
ㆀ O
OO
이
.
"
,M)
,w . s
d
q unlenowns
7
=
=
h Q) 3
.
bzQ 2 ,
.
[HHI
.
넓
이
.
f
" .
ㆁ .
\
-
2
=
∅
+T .
t
µ=4 N 4
(
)
=
Q~,
∅
-
.
.
1
+ ⑳=
4
hs
2 =Q
공
=
3
-
.
.-4 n * 1
T
.
{
πj
+
Fi je
= .
ve
R① 2 2
.
、
"
(
*맺
)
않
solution
⑥
technique
diagonal matrix
( ' .) .
bver
.
.. .
.
.
( =(
trianswlar metuilp
* ) (.) 대)
(미
.
5.
trrang
( ..) (
)
pper
①
*
elimination
Gauss
(
4x2
x
-
3
=
,
xy
2
-
to
make
apper triangular matrix
( ! ] [.] 대 )
O
6
xrtx3= 1
2
8
O4 시
5
x tx2 tx3=
CG ㆍ)
→
경용
)
다
)
tworom
.
.
)
(경
다
"
)
.. 지
이
②
.
enterchonge thetprot
(
Ssubtract twicethetirst vow
..
(
mnsernati
.
p떤
or,
(
augmented matrix
04 +
:% ) I
1116
2
-
21
s
o
ε
x =1
.
,
에 이행
+
OO
x2 = 2
6
1
ㅥ
-
x
3
,
β
2
=
3
다…
.
「 .
[
au aar
O
GGauss
az
ancanz
-
ain
-
-
ain
CAan
.
)
이"인)
. .
.
.
Sondan elimi natson
E
.
-
-
.
.
~
Genenal matrix
systes
A
). .
.
. ..
)
to
eliminate au
,
baa azula
Multiplythe trst row by la
.
,
and subtract from and row
.
ar
s
o
Continue until all elts
ave
eliminated
belowan
(
졌겨
w
kl
)
⑥
ana
-
py
same
way
Cwe dropC) for convenience )
(…
망인 폴의
a(2
s
-
backwand
sweep
Ais
en =
5
=
정a
.
bnlann
scory = cbny
x
]
(h
;
-
-
an+ nen)
lan ins
-
ajk ) [ a;).
*
럽
= nt n 2
-
5
.
,
"
,
1