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expansion hj-xjn-sgiqridspae.mg

h. ⁼ ^h ,

= h ^{. . .} ^:

Uniform qridspaa.mg

(2)

千唎二

^패가

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tinte.t_s.tn

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(3)

지

Ts

substitutethioimt0diee8o.g.on_-tio@j.Tjt

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⁼

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' boundary ^and ^.

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{ ^푸듮 _; I _System _of _algebra

^.ie

.

→

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^, ^-

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1돲 _: _i

j ⁼ ¹ ^: ^T2 ^- (2+55)

T.to?=hRQ

^,

F-2 ^: ^T3 ^- ( ^" ) ^도 ^t

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tre ^matrix

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qridspacimpiyi2nd-oidenFDM-s@P.iFii

( M^-1) ^X (^M)

(6)

→

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ij

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(7)

mode to

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trans dar ^matrix G뀮0기 ^剡冷 ) ^I

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^matrix

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(11)

⑤

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^Axis

Axis

A ⁱ

fill

^matrix

an

a,

씊액

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(12)

fotdmultiplicatmsn.tk

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required Gang

for ^h^가 1 .

(13)

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_Count_S

.

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drag

_ole

^and ^matrix

f

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dimimatedz.ee

^-

^愼腦 ⁵

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h j

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→ n D _, ^CN-17M ^, ⁽ ^7-1 ⁾

A-so.cn ₎

(14)

Atl options

^: ⁽ ^2m ⁾ ^A _, ³ ⁽ ⁿ ^→ ^M ^, ^{3 CM} ^A

⇒

amazon.msfntritagonalmatnixsystem.lee_lss.TT/

⑥ Computing

^inverse ^matrix

A

^B ⁼ ^I ^B ⁼ ^〔 ^스 ^. ^,

^스

^, ^- ^- ^; ^En

)

AB ⁼

(

^A ^모 ,

A 스

,

. . .

,

A

In

J

⁼ ^I

→ A h ⁼ ê ^, _, Â보 ⁼ â ,

. . .

, ABn ⁼ ^en _,

약 麾步

Ang

mental matrix

f A

e_, ^e.es ^{. . .} ^en

)

⁼

臼巧

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on His _a

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^matrix ^.

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^? ^恣活

tri-diago.cl ^matrix

(15)

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of

â ^based ^matrix îs â

^he ^matrix

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^:

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^each ^{M and} ^A

cell ^matrix ^A ) ^~ _sine

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^LU

^de Composition _Ax

⁼ ^b ^→ ^x ^.

^A

^' ^b

Ax

⁼ ^b

E

^sur ^UTC

effect

^→

^{毖咨 엢} ^;

(16)

Operation ^엉 multiplicationqoneron.by

^a ^constant

and ^sub^tract

^from

^an^other

rowcanbepe.tn ^med

by

^a ^matrix

multiplication.e.g.mu _H.ph

^Ist ^ro^W

^by

^ez^, ⁽

^에 ^a

^.

⁾

^and_and

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ro^toW

.

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테테 二鬪 ₎

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(17)

To

eliminatethelstcol.rs

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ㅎ

di

^min^ate e

any His

^below

at

^↳ _o

톃讖 i ₎ ei-ailaiEE.AT ^戀 ⁱ

→ 퉤 ^텀 ^.EE, A ⁼

Lf

^"

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-

= E ^: Tower trans

dar matrix

EA-0

^- ^A

^낙 熬 ^A

⁼ ^A

Let's and

Ez . process ^.

E리

(18)

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multiplgstrowbyeziadaddtozndrow.it _戰沙 ⁱ

^.

^i' ^핪 ⁱ ^,

E A ⁼ U êt Ê ^na Ên^-² ^- ^- ^{E A} ⁼

U d

A ⁼ E^'

^털

^' ^{. . .}

Et ^Et

^U ⁼

^LU

nthlhhhhs

Lower trans

dar

^matrix

)

에 ₁ ^'s ^on then ^Main

drag

^on ^al

A

^a ⁼ ^b ^→ LU ^x ⁼ b

non

Z

(19)

岾戀燃淵誠油

forward swap

ⁱ ^z^,

t.be/lyEj=Cbj-tljkZDlfj',F23ii7Ux=Z:backoardsweep

^→

^an

^to

^set

^가

LU

iexpens.ve?Ax=b de

^an

position

^→ ^x ^→^.

^A'

^a^b

^P ⁾

LLU.ES }

directsohtma.it ^堆了

↳ ₍

_U _much _ear

(20)

What

if aya ⁼ ⁰

?

懺憔代昭邕籠驩 _쎊

→

Ax

⁼ ^b

→

PAX

⁼

B

^- ^LU ^x ^-

-0in liii.is

Band똎

del eq.numericdcssystemofalqebraiceqs.me

①

Ordinary de'

q )

-0in liii.is

internal

adiscretesetofcpoimlcfxj.jo

h Grid points

Tag

F

Method

)

Taylor

expansion hj-xjn-sgiqridspae.mg

Uniform qridspaa.mg

千唎二

쏆 j살h쀏상 뭵삺뻈 i

lez

兀弘

제 in

23앪나 삼 P얆 )

tinte.t_s.tn

leading

as

lens :

Tin

汁吼

27g

5없지

금새 앲 %

ㆋ呵戟쬳감 ⑤뛢

leading

이서

Ts

substitutethioimt0diee8o.g.on_-tio@j.Tjt

'다卨 一付

Qi Tr

{ 푸듮 ; I System of algebra

T+

(2+522) ftp.5Qj

1돲 : i

T.to?=hRQ

T.tt?Q2:F.N-1:O-

59mg

.

(2+55)

5Q

iii.

膝派 .it

) h훼

tri-diagor.nl

element of

drag

al

↳

from

잉

diffleqs.tn

drag

al matrix

[ ai.bi.ci

Et

tre matrix

( 籤趨 斷힎 O燮

PDE

partial del

DO i

騈ㆁ 一闕

t떃飜 i

)

杷琨

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qridspacimpiyi2nd-oidenFDM-s@P.iFii

펴 j

.it 펴 j tijtttT.jo

ij

.fi

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23앪나 ^삼 ^P얆 )

^as

^이서

_'다卨 _一付

_Qi ^Tr

{ ^푸듮 _; I _System _of _algebra

1돲 _: _i

^59mg

^5Q

膝派 _.it

) _h훼

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_drag

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tre ^matrix

( 籤趨 ^斷힎 ^O燮

partial ^del

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t떃飜 ⁱ

^杷琨

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프 t_ittoOE.it ^5Q

4-퍼t ^玉十址

^L0

( ^챻윥웒 )

drag ^and

( ^횮 ^; ) ⁽ 訃妙

^matrix

trans dar ^matrix G뀮0기 ^剡冷 ) ^I

^Make _arr

^dar ^matrix

燧烹 _:귨혊i 爬剡

북 ubtracttwicethetirstrowfnmlastrow.IO:1 代賦訛悧

Stop ^of

aug ^mental matrix

ntinuewtilallelts.be/owauareelimimafed.i::: _ai.im _慽炒

^Way

^dr.pe

셩양 ÷iㅇ燃憔怡 ^.

Operation cowtsfnobtaim.mg ^Solution of

^一峀

穩慂 ^: ^饑銷

F G0 ^앞

慽貸 _.int

⁵

^P

_이 _P서

^ㅎ name매기