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1 ) 'APOSTROPHE*» 'EDIT' * 'DESCRIPTOR'

i 3(A,1X) )

DESCRIPTOR

DESCRIPTOR

f?l];ilirDON'T BE AFRAID ^ J: 9 1-D 7-f

■ (~#<.

2)

,'DON''T BE AFRAID' )

, ISHDOH'T be afraid ) O B

'^Ih \> 4-^ ,4

m iiiiiiiiiiiiiiiiiiniiiiiiiiin>

7^% h = 7tU2X'%tX, v=sinx<7)m^-^ihX, (x, y) ^ y'i

-^ < 7"o 77 A .

0 tlx, ^^J}(r)32^i±x t

h 102fiTgS-C'«61ffT^(-J/^om$:Tl2l<^4:Tt-7*D y

42m a 72m B ^{102m H 130RfB}

32m -1

9-2 265

{i^x^27c (r>mMX'y sofiSii-1^1/^1 t£<r>x\ 30^+31.5

tLfzi,<r)^3 t-th. FORTRAN :fcT-J h t, J=30. 0*Y

+ 31.5iS=ttT, ISJ^ei T'^,-2).

y J X'^-i. hfih. x ^ FORTRAN ■ X<r) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Xli, 4-t h ixfz x h = 7r/42 i>

LXj&V.

ni.t£, x=0, ^(iX-0. J=31T-^. '), x=lX7r/42. y=sin(l X ;r/42) CO t

^(±X=lxh = lx(7r/42), Y=SIN( 7r/42) = . 07473 T'. J=33 . 74=33 i ^-5 .

■ r^xh-h, X=0. J=31 60;>;co^Tr(iJ = 33<?)^(-fT.^.tS .

9-2-2 yp ^*'7

(1) 7 LTGRAPH i 9 Xm^W<tzih

\ ^AKTi;<3t^M»^-^^XAXIS,

7' ^ l"i L. /, t

\ ****** 'CU^VE PLOTTING OF SIN(X) *****

000001 Nv fCHARAClER GRAPH*61/ XAXIS/ YAXIS

000002 JPARAMETER (PI=3.U1593/ A = 0.0/ XAXIS=' I ', YAXIS='-')

000003 \PARAMETER (B=2*PI/ H=PI/42)

OOOOOA DO 10 1=1^61 I

000001

000002

000003

OOOOOA

000005

000006

000007

000008

000009

000010

000011

000012

000013

OOOOIA

000015

000016

000017

000018

000019

000020

000021

000022

000023

000024

000025

GRAPH(l:i) = YAXIS

CONTINUE

WRITE(6/600)

FORMATCIHI/ IH / 62X/ '*** Y = S

& IHO^ 40X, '-1', 29X/ '0'/

DO 11 X=A/B+0.001/ H

GRAPH(3l:31) = XAXIS

Y = SIN<X)

J =nY«30 + 31.5}

GRAPH(j:j> = '*•

WRITE(6^601) X/ Y, GRAPH

FGRMATCIH / 2E167r8/ 9X/ A)

IF(X .LE. A)

8 THEN -1

DO 21 J=1^61 I

GRAPH(J:J) = • '

CONTINUE

ELSE

GRAPH<j;j> = • '

END IF

CONTINUE

STOP

END

0 9-4 iz-sinii^^f^yyirtiyJJt&XoXyjU

SIN(X) ***• //

/ 28X^ '+1' />

559# -X ^ >&

0.0 0.0

0.7479»J 76E-01 0.74730039E-01 0.14«t»955E<00 0.14904213E*00 0.224399 33E«00 0.'222S2077E<00 0.299199 lOE'OO 0.2947349eE*00 0.373991 OOE'OO 0.36534077t.00 0.440796 &6E<00 0.43300349E*00 0.323396 43E*00 0.49999970E*00 0.590396 21E*00 0.S6331974E<00 0.67339 9aEtOO 0.623409S0E<00 0.747997«E*ao 0.60017244E<00 0.0227934E«00 0.73305134E400 0.0973931E*0Q 0.7ai83115£400 0.97239 09E<00 0.02623e39E<00 0.10471964E>01 0.86602479E400 0.11219S9E»01 0.90096619£<00 0.11967 S5E«01 0.93087310E<00 0.12715SOE'Ot 0.9S5S7219E400 0.13463 43E>01 0.97492743E»00 C.142114ie.oi 0.9088304SE400 0.14959 36E«01 0.99720353E400 0.1570732E»01 O.lOOOOOOOE'Ol 0.16455 27E<01 0.99720401E<00 0.17203 22E*01 0.98a63134E400 0.17951lOE'Ol 0.97492BB0E4OO 0.1069913E>01 0.9SSS7404E400 0.19447 OOEtOl 0.930a7S42E400 0.20195 04E«ai 0.90a97094C400 0.20943 99e»01 0.86602795E400 0.21691 93t>0t 0.a2624165E40a 0.22439 90E«01 0.70183508E<00 0.23107 65E«0i 0.7330S601E«Oa 0.23935aiE'Ol 0.68017739E<00 0.24663 76E«01 0.62S49304E400 0.234317IE«01 0.56332376E400 0.26179 67E>01 0.50000626E400 0.26927 62E<01 0.433a90S2E*00 0.27673 56E>01 0.36334026E400 0.20423 33E*01 0.294762aSE4a0 0.291714ac>oi 0.222S290SE*00 0.29919 44e<01 0.14903077E400 0.30667 39E<01 0.74730979E-01 0.31413 34e»oi 0.92109921E-OS 0.3216330E«01 •0.74720621E-01 0.3291125£<01-0.14903239E400 0.3363921t<01-0.2223miE406 0.3440716E>01 -0.29474527E400 0.33135llE'Ol -0.36333111E«00 0.35903507E«01 -0.433B73a9E>00 0.36631 502E>0] -0.4999902aE*00 0.37399 97E<01-0.S63310S6E400 0.30147 793t«01 •a.62346062E*00 0.30093700E<01-0.6aol6392£»00 0.396437e4E»01 -0.73304343E»00 0.40391 779£»01-o.7eie235aE«oo 0.41139 774£401-0.B2623U2E4OO 0.41607 770E«01-0.B660ia71E*00 0.42655 765E>01 -0.90096293E400 0.43303760E>01-0.930e6B6«E«00 C.44131 756E>01 -0.95556B67E«00 0.4407973U«01-0.97492474E«00 0.43627747E.0I -0.98B82B60E400 0.46373742E.01-0.997202636400 0.47123737E.01-0.10000000E401 0.47071 753E«01-0.99720496E40a 0.40619720E<01-0.98083319E400 0.49367723£«01 -0.974931406400 0.30113719£«01-0.9555776IE400 0.30065714e»ai -0.930879a3£400 0.31611 710£»01-0.900976106400 0.52359705E»0l-0.066033976400 0.53107700E*01-0.026240596400 0.33033696E40t-0.701042396400 0.34603691E>01 •0.733064176400 0.33331606E>0t -O.6BO1062764OO 0.36099602E>01-0.623S0446E400 0.56047677e.01-0.563335766400 0.57393673E«01-0.500016696400 0.30343660E<01-0.43S90157E>00 0.39091663E*01-0.36335949E-00 0.39039659E«01 •0.294774416400 0.60307654£>01 •0.222540066400 0.61335649E>01 -0.14906275e400 0.6200364SE*01 -0.747510196-01 0.62031640E401-0.212020166-04

tlXis

(2)

( i ) Y=

(ii) :S;

(iii) ^

(iv)

i219-4 i}<,

4

5

6 10

9 • 5 i?=sin

51 a

... T ' «IHCX)

9-2

ilTiJ YAXIS itS.

( 2 ) $r A=0 J&'f. H=7r/42 cO^J.^iIiiT-B=S a- t V^tr>k<^z t

( i ) Y=SINCX) r-sinx(7?fit?:^i^, -t Y C L T J=30 . 0* Y+31. 5

x-Y<^i$.tpmt j .

(ii) iCPm'St^GRAPHcoJ^Ui^-Xt-^^lz^li..

(iii) ^^X tY t GRAPH ^ h .

(iv) GRAPH

i: L. ^[±^-|(tGRAPHco J#g<7):fc^^* ''ilt ^ C S ^

m9-4/)<, z.mFORTRANXxm^^ki,<XtX', ^ ^ ® 9-5 I219-4(7)7*c

1 CHARACTER QRAPH*61, XAXIS, YAXIS

CHARACTER i -7 (hu GRAPH t XAXIS t YAXIS i v> 7 t LX^

GRAPH* 61 II GRAPH t -} f ^tRi Z t ^^1".

2 PARAMETER (PI = 3.141593, A=0.0, XAXIS= ' 1' . yAXIS='-')

3 PARAMETER (B=2*PI, H=PI/42)

?£~T-^iPI Ii, TrtOjfiiUfti 3.141593 LTfitiffiti C t

f^tl^l;Ali^&0.0 $riSL, :4:'fM^^^-^XAXIS ll-oc?>^im?? '

t • [ I:. YAXIS II1 :$;?

3tT@co^--"7 / —^':S;^±, B ^■ ®|^2>f3 . 141593=6 . 283186, H^:^|43.14 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

1593/42=0.07479983 LTtm1-^.^a:^:r-AaA^ 2'i7SX'tXtz

5eS 3. 141593 ^ PI 1 7 t A'M ^ tlX h<r)X-. 3^^X'i±^^^(7i

141593 i»< ItJ:) >) U PI ir^lti.

- «1 7 UVd ^7 AT-fi47 *) S^T'

4 DO 10 1=1,61

5 GRAPH(i:i) = YAXIS

6 10 CONTINUE

9.5 y«sinx«o/7 7<^aii:

S^&GRAPH 61 i- YAXIS cO - I: ft A "f S DO Zt T" S .

- ~-C- GRAPH( i: I) (JGRAPHiO I <r>:Si:lPU'9)-nX'h i . tKfhh,

GRAPHoi L-c^&Ja^o^ScYAXis <7)r^^$rftAt 2.:fc^ftA:!:;!''

GRAPH(i:i) = YAXIS

^n^i=i't'-'^6i ^-c-DO:g:r-^oi^-r.

WRITE(6,600)

600 PORMATdHl/ IH , 62X. '*** Y = SIN(X) ***' //

& IHO, 40X, 29X, 'O', 28X, '+1' /)

•7 f > 7*'J y ^ f'l-

63 64 65

I « I * I _♦ I

70 72

I IslilNKlxi)

^{* * *}

tf-mt, 4im@ t 42mUi--i, 72^01-

0, 101 firS t 102t?T9(-t± + l. i -en-ffiFn^'lt i .

72 73 74

lol I I

100 101 102

nmi

DO 11 X=A,B+0.001, H

X A^^hBt X-M^ViUV^ tX, ^ CONTINUE i

nau. t, i ^ • Ed'U.

5gM^

10 GRAPH(3i:3l) = XAXIS

GRAPHS 31 XAXIS C7>1^^ T-#) 1 $:Alt4ftA

Xx-hh.

ZZX' GRAPH (31:31) GRAPH co 31 # g 31 S @ t

f3f>31#g^:ii:^^^t.

Y = SIN(X)

; J = Y*30 + 31.5

X^iatcHtSSINCX) -fc7>^g^^Y(-ftA1-4.

A y-f^) y ^±-C'<oEnSijI2;a$-^T^&J $• 4i. 4ft A:3:T'#? ?•.

YAXiS't'i;#,^.S:^co- D03tT-^,5.

[± GRAPH V ^

LX^S1(^^^YAX1S

YAXIS

61 tx-DO-X'cm')mt.

-—-

IH , 62X, '**+ Y = SINCX) ***' 11

40X, '-1' , 29X, '0' , 28X. '+1' /)

• 75> Ife x. T 63 @ 80 S ± T-[I

65 70 72 80

* I |Y| 1=1 |S|I|N|(|X|) I [*I*I*

±+1.

72 73 74

lol I I

100 101 102

rTTTTl

31, H

IX, :fc#-^;bai CO CONTINUEltS-C$—0(7);i.

;T-B (Oith 0 HB+0. 001 ttc^x^^i,x>li, t

? il ^ T- DO X hi>Zt ii^f} <* tzahcn t cof h. —

L^'L,

i, .117) l T ^ir>iL^gfi{l .

XAXIS

XAXIS cof^#-C-^>S:SC^SS:co I S-AnsftA

51) (l2£&^A<GRAPHt7)31#g7{»>ib31Sgc^:5:^gB^yiJ. t5:

X) iz^iULX, iziXAt ^COY

9-2 x ^ m m <7) i& m m jgt

Y=-1.0 CO It J=1 #@

Y= 0.0<7)t J=31#g

Y=+1.0«Ot ^(± J=61#g

31 co-ftfc 0 {; 31. 5 i 0. 5

3°y+31 'OtSS:(:JlzXtl 4 i #.J-SfiHT 1 IBB s H»£A L TSStti 14 4 .

13 GRAPH{j:j) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ■ *■ ^ '

J'^mt'm^tzcov, :^^&^GRAPn<7):ic^^<r,j:^^izn'^mx>:Sc^i:LxXc^i^

WRITECe.BOl) X, Y, GRAPH

15 601 FORMATdH , 2E16.8, 9X, A)

X 2: YsO®$-f?®j/J^|{r,t^^-C-Ef]igijL^ ^^^mgfeGRAPH(7>

--X, M.iil L ^En^lj L X A=0 .Qcot^i X-co^:\)McO^^ (42 ffTg~1021ff

g) iiTiaoj: T

*** Y = SIN(X) ***

IP(X .LE. A)

THEN

DO 21 J=l,61

GRAPH(j:j) = ' '

CONTINUE

ELSE

GRAPH(j:j) = ' •

END IP

17

18

19 21

20

X A imj)) graph £?)S:??ij$-^gliSeizMLrfe<.

X+Acoi# (;A(1]) t'hi^mw^h^tzt^lzlt, graph ^:3i:^?iJ<7)j#g£7)* ,7)Sp-g.

S-Sei3^L-ri5 <.

?>rv -y 9 .

23 11 CONTINUE "

24 STOP

25 END

_ 23fta9'nsnm-xtzm'tm*xv. ^nXix-i'DO,<.-rt(,i

****** curve plotting of sin(x) and cos{x) ******

character blank, graph(61), xaxis, yaxis(61)

parameter (pi=3.141593,a=0.0,blank=' ',xaxis="r)

parameter (b=2*pi ,h=pi/21)

do 10 k=l,61

graph(K)=blank

yaxis(k)=' -

10 continue

opendO, f ile=' graphl', status=' unknown')

open(11, file=' result", status=' unknown')

write (10,600)

600 formate '/ ih .'y = sin(x) -> * . y = cos(x) -> +' //

& '-1* . 29x. '0" ,28x , '+1' /)

write (10,601) (yaxis(k). k=l. 61)

601 formate '.61a)

write (11,602)

602 format(lhl/lh sin(x) cos(x)

do 11 x=a, b+0.001, h

graph(31) = xaxis

yl = sin(x)

jl = int(yl*30 + 31.5)

y2 = cos(x)

j2 = int(y2*30 + 31.5)

write (11,603) yl,y2

603 format (Ih , el6.8,5x. el6.8)

graphdl) =

graph(j2) = "+'

writedO, 605) (graph(k). k=l. 61)

605 formate ' .61a)

12 continue

graph(31)=blank

graph(jl)=blank

graph(j2)=blank

11 continue

stop

end

+ *

♦ +

♦ +

^ + <- (X)SOO = A ' * <- (X)IITS = A

parameter (pi=3.141593, a=0. 0, ramlxla=l. 5)

parameter (bl=10.0*pi .hl=pi/100)

parameter (b2=13.0+pi ,h2=pi/100)

opendl, file=' result2-r, status=' unknown")

open(12, f ile=' result2-2', status=' unknown')

outputformat zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ■ .5x. •

do 11 x=a.bl+0.001. hi

yl = exp(-x/rainbda)*sin(x*10*pi/ranibda)

write (11,603) x. yl

603 fonnat (Ih , el6.8,5x, el6.8)

11 continue

do 12 x=a. b2+0.001, h2

y2 = (x-25)**2*sin(2*x)+x**2/2

write (12, 604) x, y2

604 format (Ih . el6.8, 5x, el6.8)

12 continue

close(ll)

close(12)

stop

end

fd'' A=/.y . QtoL^/ofL

Source

t>^zS _ex2.exe ^hesult

Result (

result2 1 vs. row

500.00 i

250.00

result2 2 vs. row

^'{x.-2^f/i^2X- -f ^ , OiX^I3/l

Source: e;(ecHre result

e'A2..f ex2.e/e i"&sulfZ-2

deduced

(1) AU_U((n+l)At)-U(nAt) . _{l^J At ji = iO}U(nAt)}

(2)

(3) u

clU _

[1] M'^'ll^ (Consistency)

t = nAt=~^<7)T'CAx. Ay, At^OOB#,

[2] (Convergence)

B?^yt = nAt=-^COTT^AVAti5J:t/Ay/At^-^^L7-f^Ax, Ay,

e - I On —Un I -> 0 ^

(1) X n

Un^I=(l+icoAt)Un ^ iuy-t' •

Ui ={1 +icoAt)Uo

U2 = (1 +icoAt)Ui

1.

2. pf^ -t — K

[3] (Stability)

Ax. At-7E®^)tT% tSritpi^^CLT-ctl.

|U„|<K

Scheme

(l) (Euler) scheme

tuler S cf)eme T L/i •

Ui = £) ; I X /" + 0.2^ 17^'''^ Z^" I

U„+i=(l+icoAt)U„

= Aef'U (= e'®'^'U )

1^1 = v/(l + icoAtXl -4o)At) = V" 1 + (toAt)^ > 0

(2) ®;S' (Backward) scheme

Un+l —Un _ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

^"■ ^1" l-iCOAt^"

Uni 1 - U ((n 11) At) ; t.

B . s4e»e T I? l/i

Ur 0^1^585 7^ A O.^T-B-QO^JO k/O' i

l^h . I ,<l

V 1 + (coAt)

(3) scheme old b w f )

iZj (jj. li

_ 1+^ V X t,<'v-, \'~ Ti

~ , icoAt , , , , , , ,

1 T" 0" , =1;^. U3--l)j

,,, , ^ [-.r h

(4) three level scheme i f . ' ^1- ^ '

■ -?'r ^.r. ■ ■ ---:

Unj.1 Ur. 1 . \ \ . . .• . . -\ \ +

Un+1-U,i ] ...,,, , ,, , = iioo(U„ + U„„) ht^ i

2

'n+1 ^n

—1_ -.^Tr t'

2At ~

U„+i = 2ia)AtU„ + U,_/

nt* ~ Ufl -1 = Z 0; Un 2 At

^li-1 *-2 2 COAtt^ni* Un-1

(u, =U, =1)

-n^ V ^ ^ 1

ex3-l

complex AjUO.Ul ,U2

real T.deltaT,omega,f

A = (0,1.0)

T = 0

UO = (1.0,0.0)

delta! = 3500.0

omega = 2.0 ^ 3.14159255355 / 65400.0

F = 5.0 * 65400.0

U1 = UO

U2 - (0.0,0.0)

open (5,fi]e=*rlt3-r,3tatus='unknown')

do 10 i=0 ,f,deltaT

T = T + delta!

U2 = U1 + A ^ omega * U1 ^ delta!

write (5,100) T,U2

00 formatClh ,el5.6,5x,2el5.6)

U1 = U2

10 continue

close(5)

stop

end

Euler Scheme

100000 200000 300000 400000 500000

time

ex3-2

complex A,U0,U1,U2

real T.deltaT,omega,f

A = (0,1.0)

T = 0

UO = (1.0,0.0)

delta! = 3500.0

omega = 2.0 * 3.14159255355 / 55400.0

F = 5.0 * 85400.0

U1 = UO

U2 = (0.0,0.0)

open (5,file='rlt3-2',status="unknown')

do 10 1=0 ,f,deltaT

T= T +delta!

U2 = l/(l-A^omega^delta!)^Ul

write (5,100) !,U2

00 formatdh ,el5.8,5x,2el5.8)

U1 = U2

10 continue

close(5)

stop

end

Backward Scheme

100000 200000 300000 400000

c ex3-3

complex AjUOjUl ,U2

real T,deltaTjOmega,f

A = (0,1.0)

T = 0

UO = (1.0,0.0)

delta! = 3000.0

omega = 2.0 ^ 3.14159205355 / 80400.0

F == 10.0 * 80400.0

U1 = UO

U2 = (0.0,0.0)

open (5,file='rlt3-3',status='unknown')

do 10 i=0 ,f,delta!

! = ! +delta!

U2 = ((1 +A*omega^delta!/2)/( 1 -A^omega*delta!/2))^U]

write (5,100) !,U2

00 formatdh ,el0.8,5x,2el0.8)

U1 = U2

10 continue

close(5)

stop

end

Daikei Scheme

200000 400000 600000 800000 1000000

c 0x3-4

complex A,U0jUl,U2,U3

real Tjde]taTjOmega,f

A = (OJ.O)

T = 0

UO = (1.0,0.0)

delta! = 3500.0

omega = 2.0 * 3.14159255355 / 55400.0

F = 10.0 ^ 85400.0

U1 = UO

U2 = (1.0,0.2517994)

open (5,fi]e="rlt3-4',status='unknown')

whte(5,90) T,UO

90 formate 1 h ,e 15.8,5x,2e 15.8)

^ do 10 i=0 ,f,delta!

! = ! +delta!

U3 = 2^A^omega*delta!^U2 + U1

write (5,100) !,U3

00 formate 1 h ,e 15.8,5x,2e 15.8)

U1 = U2

U2 = U3

10 continue

close(5)

stop

end

Three Level Scheme

200000 800000 1000000

(O -s. 04-> ^ ,4c^te.«tje- /2 '^.u'^ C^...

( rt zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA '(■ i fe"} _

^v\+» —Cii~i « , t )

■ I - ^(a»L/h

^.A-t

lv

Oh<^i ' Ow-^ -v iC 0}/\

in Oft ^ 0( "t. Oi

rT' , -&T5

01 ~ A Oo

02 = ;>^Oo

Ov^ - A Oo

-cTin? Q)^^Kx C t;'--> 9 t ^ Si

Oo ^ X "" (Jo + 2 C p a!^ U,

"fc /A"' Ott € % ^

x" = I + i L P A

r A, - ji-f" t cf

I /1v- = -JT^ T^-f

^ 0 "c . f' .<^^1 -^0 'l"3 ^ T'

A ! -^J__

y\i -^ .-

5- " J~' 'TilffcL^

" P' CzrM^l>Ctta7Vx£- ^m/scU^

-t -c Alt A Q_o = ^1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

■ :>5=-'J , /V ^ 1-^ A' . .

II . . 1 i 1

\ \ '. M

< t^ '• ' '

n/

3^1- 1^tc^

T? ^ - Sl y-y 'I/- +7 < . ^ H- ^ -

Ow - A^ —^-

Om -vT 0,0 0,0 ■ A iR."^!'"*-

O.V. '= A o.o _ O.0 ■• at

© -^ Un = A Ai" Uio + 5 Ai" U20

(p. @

f 0& - . A ^ ■

|0\ " AA/ tJ'O BXa. OjlO ,

^ o

U,o , 0».o r-T^vl -<1 ii^tc,j^ . -V .

A Oio = ——! (^0\ — Ai^o^ I

A0,« =

xo » — f O, - A, Oo)

= A A," 0,0 r B Ai' O;,-0 A a

A/ ~ A; ^{(^^O, - X,XJo')}

^.-F' ItJ =e.'F'

1 0.,_- Ai Oo 1_<M ■ M% -FO Aj^7^<

i" 3La't= 3i '), ■ i-t%-^ ^-t" ^ . f<

Ots ^ I e^" f \K i-y" O X n <- ^% f l- <;y -fc

^ ± Ox / X

^1

*3) t\Aler 'i.*' OotS> '5) l)J4

00 , O 1 —^ ^ . I'fI. IT y-: >5 > tK ^

A

r' Oo ^ O \ I

® OD,Ot -^0> "t iqll t ~ ^ /

„ a

^'n i'j-h ji yXt -i A\T

'i^*- ■ d'U ^ ^ V I I ^ r p-FA

r -K-O : U C,e . .

rjy'A-'JiH C^.ZHB >t

s>x^

c-^ ^{U At}

ac//^~^ t~^~''

[j- - .n^t)

(J=0 C^./1>) i

itl % T^y "7' zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA -■ - '7\ <3t (^ -Vl -O, 1/2, ---3.

•^rB)XT-y7'' ■ •■ I AX C C = 0, t. 3. - ■ ■ ) .

0, -0 , -n^tj) ^ f . .

3 A. laj vr/ii t 6 ^

C - ^ or - 0 - £■

Ml

5C'^X^»'v^<^ l"J .

or' - or'

' yt. ^ .

(|) b, - O^

f^>CrhUyi ^}

-fr c - 0

t-0

3^ X t^rc

rt , 1^

Oi - 0_Mi

^ 0

fltrT] t«ler(-fWw;

^ ft-ri A

@ be - Oi ^ c.

•1 X ^

Uiri - Ul

jLcuryvc^C^^^stvvv

Co 0 )

C C < O ), .

0 . ^{li<^h}

l-i t tt/

Oi = 0;_

^ ON

^ c COc^, - Oi-i )

Ot^i ^ _0;h ® 3w- -6^yiO;, (%t

<S ,_<$ i- iM-ic

■ n - 0, 1 ^ ^0 >3>) i--\',T7 . .

.i««. €^--77' z

- /c^ -7 . Z3 ^ /Sf

3 ijZ- . L : ^ a iX . 5'C X 50 7^^/S

" I ~ _{^ yJ-}

zst " ^ 7' ■ *? V • t ~ rt 1'' 3"^? 1 ■ .

> -L

^t" C NeuvMrtAw^ ^ ^ .

'» ?• ^-ft'M ^

■ f '';a^ t li PP^ ^ /v (SJa:%.i-7)if5-;?iliK ^ f^iii->J> U->3>5^5->vrt

f, 1 Jl T tX t '3 - ,

I = 0 ^5^ X ^ 9^^ {.X

■ ft" ^ J <, TT ■ *"' ^ 7

i;v-3 : t

o ii T<'5 ^

TSKI, "'' « >

:i :f2|

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e./t C'Pi)

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r< ^<

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^ ' <1^

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r<

Nr

o- -<^

tQ +-^

-c -®^ — — I

-C- • •-

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SI

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t-

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I ^*■

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

- ,f] -

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i _ ..

— — I— —ft

0 >-0

- U) bPJiSWAlO |J II !/y \f^ Ib

y)^ IZ ^ IZ

^ u'^ - "Jn Jn - „;n

© '1 -

"V. ^ ^ sUA^ '-y I >a M

P Vf;f^, ^'Z^^rroTTM ^ -IT^r^ T.

{ f l .^3 '5 I ^ -( 'i' _?■ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ^{>; -}

u(09J4-S(l/) ty^ m u

-o-<-i 0 - -T-r^^^-TTT^ +

Vi - - n

U. ' u '

IV

■ n -, Jn

(f)'1 - -t Y

(in

('p-;n)^T--/n--^'n

( - n - '^-_o'n " 'n

(;n-/n)^.^;n -;n

^ - zn)^j- ;n- ;n

¥i^'¥

(.'n

cn

(/n

(:n

Ifff

;n) 7? 5-rn

f -I ^

:m#-o37n-

-:n-)^o-^:n

-in

Tvf

XV

. ^ !>.- - — b——>—f' »

. J._ ^., _

tcTkC

ZmfWr "/J Yi >

,'n

(70 - ;n)#y- /n - /n

Jin-;o^m2-JD -:n

Y ^7

ryi- - .'n -

I7n -jn) H 0 - :n - -.'n

JJJ X , t

_U (50, M

A/i Mm H

t = (? t t =_c,f n u(x, 0) ^L)(x, (x/i/ 1:

-^J1M-1 h. At "A I

'-0 L t-'J ^^t^ U(A, ,V(j, IJ ^V(J(x,2j t Iff

n. At - A I

jt = 7 T t -2 <0 1 ^ U(ic Aj, U (j:, 2) i, u(2 ,11111 ^

15 A I

—i^/Mt'VjTo'Ar^ - - ■

^ ^ b <£- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

□ 2(^)10)7 . j

U(o.lo,0:ro) t- 0'-5'0 ,1-0-^90

deltc\ I 2

del to. I

c/e(f<\ X

t -(7.1"

t-

delfcjl = jr(70 (sec)

cle,lt<2^1 ^ /OoO (Sec)

t--OA, 1^50 fxilL -lie/MX = C'^i

in -df

00 /o L = 0 . so

IM1,0)_=0

/_0_CoMiNDl_

_ Do 20 1^24,26

U(LOJ_^/

2_OX0(/TI (JE

Ufo, 0) Uf50. o)

AcjJ

m -_A 2 X' U (? , c) 6

— U2

UZ(<5.) - U(o ,0) 'C* rl&jti^Jl/delta/, ( \JiO ,0)—[J

! ./) 0 30 I -_L,JV _

_U2Xl) - a( 1 ,_0J -C *2cWZ/c/e/-MX *( -U (x,-A)Zri

2-0 COHJJHUI _ __ _ ____ ___ _ _ _

__ uz(0} ^ U2(7or"3

A ^ - ^ U(x,c) ^ U[X, t) UX.X,_/)JL

rt % .

_ U(.a, I) = - CMdelul/Ux^'^i^i U?(|)-U2(iro))

do 4-0 I . _

U(I, I)- U(l ,o)-^^del_t'^2/3'e/f^K U.2_[Lij)_^U2(L -l)J____

U(SO, I) = li(iO, 0)-C^c/e/f«2/(/e/MX*(U2(Oj^lj2(X'^)}

u(o, ^(Tonrr

Td—^

fttteaffiTdu

IflMILHoo 05

(i-r 0) n)^ (t-T"oT) n =iro5)n

" ^'T--l Q9 QQ.

^(jr-T' osJn - 0-T'r}n) ^ (z-t oIn = (t'o) n

J'^-Li- \^IU I

; t _

f9^7f:i; f; (o s^_05_) n ^ ^

i

c *** ex4-l. f ***

c *** iryuu houteishiki U*

adveci I on

dimension u2(0:50). u(0:50. 0:50)

c = 0. 5

deltatZ = 500

deltat = 1000

deltax = 1000

reading initial values

do 10 i=0. 50

u(i.O) = 0

10 continue

do 20 i=24.26

u(i.O) = 1.0

20 continue

u(x,0) -> u(x, 0.5) using scheie2

u2(0) =u(0.0) - c*deltat2/deltax*(uC0.0) -^u[o%0)) U(x , {?)- C) - D ( ^

do 30 i=1.50

u2(i) = u(i.O) - c+deltat2/deltax*(u(i.0) - u(i-l,0))

30 continue

u(x, 0) . u(x, 0.5) -> u(x. 1) using schemel

u(0.1) = u(0,0) - c*deltat2/deltax*(u2(l)-u2{50))

do 40 i=1.49

u(i.l) = u(i,0) - c*deltat2/deUax*{u2(i+l) - u2(i-l))

40 continue

u(50,1) = u(50,0) - c*deltat2/deltaxii'(u2(0)-u2(43))

u(0, 2) -> u(50,50) using schemel

do 50 i=2,50

u(0. i) = u(0, i-2) - c*deltat/deltax*(u(l. i-l)-u(50, i-1))

A I I I

' ^ 3

7^

do 60 j=1.49

u(j. i) = u(j,i-2) - c*deltat/deltax*(u(j+l. i-1) - u(j-l, i-1)) ^''/hi-

60 continue

u(50,i) = u(50, i-2) - c*deltat/deltax*(u(0, i-l)-u(49. i-1))

50 continue

c output

opendO, file=' rlt4-r. status=' unknown")

do 70 i=0,50

writedO,' (Ix, 51f5.2)') (u(j, i), j=0,50)

70 continue

closedO)

c —

U vs. {time, x

AX = /ooo. 0 M

A t =(000. 0 sec

C = OS

\Ji24 -It ,0) =-0

ex4-2. f

*** iryuu houteishiki no. 2***

dimension u{0:50,0:50)

c = 0.5

del tat = 1000.0

del tax = 1000.0

reading initial values —

do 10 1=0,50

u{i.O) = 0

10 continue

do 20 1=24,26

ud.O) = 1.0

20 continue

do 50 1=0,49

u(0, i+1) = u(0,1) - c*deltat/deltaxt{u(0, i)-u(50. D)

do 60 j=l. 50

u{j, 1+1) = u(j,i) - c*deltat/deltax*(u{j, i) - u(j-l, 1))

60 continue

50 continue

output

opendO, file=' rlt4-2'. status=' unknown')

do 70 1=0,50

wrltedO,' (Ix, 51el0.3)') (u(j, 1). j=0,50)

70 continue

close(lO)

/i t ^ D , " T -T'- t'- ' T ■ 7 «•' ''' i

So/l&Ane- Z

U- ^8U

rlillllillllilMltt

AX » / 0 ^

/it, = / ooo .0 5ec

C

U(2^ -IS .0) ^ i-O

U vs. {time, x )

*** ex4-3. f *+*

iryuu houteishiki no.3***

equ<xTion

dimension ii{0:50,0:50)

c = -0.5

del tat = 1000.0

deltax = 1000.0

reading initial values —

do 10 1=0,50

u(i.O) = 0

10 continue

do 20 i=Z4. 26

u(i,0) = 1.0

20 continue

do 50 i=0.49

do 60 j=0.49

' UlfO, 0))

il - - iA(4 9.

II r u(o,ol - D(a(f ,0)-

u(j.i+l) = u(j.i) - c*deltat/deltax*(u(j+l, i) - u(j.i))

60 continue

u(50, i+1) = u(50,i) - c*deltat/deltax*(u{0, i) - u{50, i))

50 continue

output

opendO, file=" rlt4-3'. status=' unknown')

do 70 i=0,50

writedO,' (Ix, 51el0. 3)') (u(j. i). j=0,50)

70 continue

closedO)

Schfne 3

^/ooO,v

^it ~/ooo < 0

C ^ - 0.5-

U vs. {time, x )

_l_ 3_ 7_ {r,o riohs force)__

\: s-jx-hAMIiJf- r:A^_gi.ii_n v h

i <0 ;TLi "7_l.v; (s]

i\ t u >0 t 1 c\cs^f_^Q.(A

UJ^L5.-K^f4L,jQ U afe ^ - -

lA + (hcer3.f SI

,1;hnr±^. \n 1 h 4f it} ^ M ^ ^ h

<^1 h ^ n UM t AM f f'- in ^jSA-^ h »Pj H v-711 ^

311331 ^ t'/ '/ f ft- 1X ^ r- 7_') ^ 1/1 T <h h.

ii = a cs^f (u t ■ llj

P 'n t - f- / h ft^' U 11 ^ vi" M u 1^ 1 , . __

dt ' df dt da it

s S_ t\i'

-Id/i^? ■ a_-t 2a^Slce^9>. -/^9']^^ -t zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

13 ;/i-jL-1^<^ IS^^ttLrlv^i^ jJ_0_Afs_ (-^iooc

/if h/h ) r h 1 'a«asi L th. A P ■> □ ■ n U % -^K

u I n x v-^, 4 a ih 1,

_ c": r i aSl A^^f = f 111__, 3 T- 'd^l/d_t_t ia ^ ^%n ^ilA

_z/ ix 3/ 'I r--' ■ ft\'7- . l-P h , _.

^-.-f£A- x__A._ /

ft- 7 4i Z , -f Th ^

^ _5 iL.t« UXM 1

j]<- oA_p_ 1 ^ P (

t>-Q J

IhJ i

;a , JQ p] \ iLjf-/3 l' \ -^ 13

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jof ^ _ _ _

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A C(?^ _

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tn i3_ ^ "^^3 L 31^ I ^KK')

i ^ t ^ fyh jk'V. -1 iLU iXb ^ 'll 73 t -M 11 ^ i73_

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1-- ifN T' it MX t M fL t\ 33_. Lx A t VI _. /!AA^.7 VJtL

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1. 7:^ n'- - V t'H 3» t >_ ^ Ii]_t jS_ f/J U r^ L .H ^ l'^ p a- m 1,

fi 1 <0 iJojL ^ t C _{■ ^Ti} zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA _{;AjU i} a TA 2 >: r~ p: 1%

A i'-2MJ ^ t X t i_\ - - - -

— (27

i--' b ih 3_.

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t« , j, rj ^ ^ K ^ 11 la , T ih I - A - 1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA _{■ • f-}

m f=i t ^ i: +v_i r^t f^R;i /3_t

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tc 4'J I.'} 1<7 113 ■ _l ^1 1, _____ _ _ -

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t v? K>4 44^13:1 Ml

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