Post on 27-Feb-2018
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TRABAJO PRCTICO
ASIGNATURA: CD.ASIGNATURA:
SIMULACIN DE SISTEMAS 337NOMBRE DEL ESTUDIANTE:
CDULA DE IDENTIDAD:
CORREO ELECTRNICO:
TELFONO (S):
CENTRO LOCAL: CD. CENTRO
LOCAL:METROPOLITANO (SAN ANTONIO) 0104
CARRERA: CD. CARRERA:INGENIERA DE SISTEMAS 236
ASESOR: PROF.
FIRMA DEL ESTUDIANTE:_____________________________
LAPSO: 2014-2
UNIVERSIDAD NACIONAL AIERTAAREA DE INGENIERACARRERA DE INGENIERA DE SISTEMAS
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T!" #$ %&'$'#&
2 OBJETI*O 4 RUNGE +UTTA...........................................,
2.1 G% %&'/$# %&' "&/ "&$/ #$ /3"%' 5 " 53$/3"%' 60 #7/ ......................................................................8
2.2 G% 5 " /$'# /3"%' 60 #7/ %&' %3!& #$!"$ $' +9 2x 107 ................................................................10
2., *$%%' #$ "/ /3"%&'$/ /3"%' #$ %&'&/
/3";'$&/ $' $" $35& ...............................................................12
3 OBJETI*O < MONTECARLO.........................................1=
4 CONCLUSIONES........................................................20
5 BIBLIOGRAFIA..........................................................21
1
2
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2 OBJETI*O 4 RUNGE +UTTA
E! "! #$%&'$ *+'!+, ' &' -'#+'& *, /' #,*,!+'$ "! #$%&,'
, "!' ,!,,' -$!+'$*'. L$* ,*#$!*'%&,* ,& -$!+$&,#,$&-$ 5",,! ,+,!' &' -'!+' , /'%+'!+,* 5",#$%'%&,,!+, ,*+'! !,-+'$* '& -'%$ , 60 '*.
P'' ,*+, -'*$ *, #",, "+&8' "!' ,-"'-! ,,!-'&,&'+9',!+, ,&,,!+'& #'' #,,- ,& !:,$ , !9"$* ,&' #$%&'-! !,-+'$* ,! "! +,#$ '$. S"#!'*, 5", +$$*&$* !9"$* , &' #$%&'-! ;(+) *, ,!$+' '& !:,$ , !9"$* 9"&!,'%&,* ,! ,&
+,#$ + = * -$! =(+) '& !:,$ , &$* !,-+'$* *, *"#$!,'8$!'%&,,!+, 5", &' '#,8 -$! 5", ,& !:,$ , &$*!,-+'$* -'%' ,* #$#$-$!'& '& #$"-+$ , >(+) = =(+)#$5", &' '#,8 ,#,!, ,& !:,$ , !9"$* !,-+'$* =,& !:,$ , !9"$* 9"&!,'%&,* 5", ,>*+,! ,! ,*, +,#$.S &' #$%&'-! ,* &$ *";-,!+,,!+, !",$*' #'' *"#$!, 5",>(+) = =(+) *$! 9''%&,* -$!+!"'* #$,$* ,>#,*' ,& #$%&,'-$$?
dy
dt( t)=kx(t)y (t) ,
$!, @ ,* "!' -$!*+'!+, = >(+) =(+) B ,* &' #$%&'-! +$+'&.
S"#$!,!$ 5", B100.000 =(0) B 1000 @ B 2 > 106 = 5", ,&+,#$ *, , ,! '* ,!-",!+, "!' '#$>'-! '& !:,$ ,!9"$* !,-+'$* '& -'%$ , 60 '*.
'*!$*, ,! &' *+"'-! '!+,$ 5", ,*-%, "! -'*$ ,#$#''-! , "!' ,!,,' -$!+'$*' ,'&-, &$ *",!+,?
C$!*+"=' "! $,&$ #$%&'-$!'& ' +'9* , ,-"'-$!,* ,,*+'$ 5", ,#,*,!+, &' *+"'-! #&'!+,''.
'' "*$ ,& +$$ , R"!, "++' , -"'+$ $,! =*"&, ,& -$#$+',!+$ , &' *+"'-! #&'!+,'' #$ "!#,$$ , 30 '*.
S"&, = '!'&-, -$ *, -$#$+' ,& $,&$ '& 9'' '&:!#',+$ '& 5", #",' *, *,!*%&,.
3
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O%+,!' &'* ;-'* 5", ,*-%'! &' *+"'-! #&'!+,''. P,*,!+, ,& '!&** = &'* -$!-&"*$!,* , &$* ,*"&+'$*
$%+,!$*.
SOLUCION:
MODELO POBLACIONAL
C"'&5", #,*$!' *'%, 5", &'* #,* = &$* ,*'$* *, #$#''!#',!+, ,*#,-'&,!+, ,! &"',* -,'$* -$$ &'*$;-!'*. N",9'* !9,*+'-$!,* #",,! '-&'' ,>'-+',!+,-$ ,!,,',* -$!+'$*'* -$$ &$* ,*'$* &' !",!8'= &' +$* ,!' *, #",,! #$#'' ,!+$ "!' -$"!' #$#,*$!'* 5", /'! ,*+'$ ,! -$!+'-+$ -$! $+'* #,*$!'*
,!,'*. D, ,*+, $$ *,' =(+) ,& !:,$ , #,*$!'* 5", /'!-$!+'$ &' ,!,,' = *,' >(+) ,& !:,$ , #,*$!'* 5", !$/'! -$!+'$ &' ,!,,' = *$! *"*-,#+%&,* '& -$!+'$. S*"#$!,$* 5", +$$* &$* !9"$* +,!,! &' *' #$%'%&', -$!+''*, = ,>*+, "! &+, , !9"$* !,-+'$*. E*+,&+, ,* &' #$%&'-! +$+'& 5", ,*!',$* -$$ H !$*,!$ "!' 9''%&, 5", ,#,!' ,& +,#$ #'' ,*+, -'*$ ,!#'+-"&'.
D$!, @ ,* &' -$!*+'!+, , -$!+'$.
E!+$!-,* * *, !+$"-, $ '*",!$ "!' #$%'%&' -$$-$!*+'!+, , 5", "!$ !,-+, ' $+$.
P$-,,$* #,$ ' ,9'&"' &' ,-"'-! ,,!-'& ''?
C$! &' -$!-! !-'&? =(0) B1.000 = &' -$!*+'!+, @ B 2> 106
dy
dt
( t)=kx(t)y (t)= yydtdy
*)000.100(*10*2 6 =
S $%*,9'$* &' ,-"'-! 9,$* "!' ,-"'-! ,,!-'%&, ,9''%&,* *,#''%&,* #'' ,*$&9, #$-,,$* ' ,'&8' &$*#'*$* *",!+,*?
4
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P/& 1 '& *,#'' &'* 9''%&,* &' ,-"'-! ,,!-'& !$* 5",', &' $'?
dtyy
dy 610*2)000.100(
= BJ
= dtyydy 610*2
)000.100(
P/& 2L",$ +$'$* &' !+,'& yy
dy
)000.100( = &' ,*$&9,$*#$ ,*-$#$*-! ,! '--$!,* #'-'&,*?
yy
yBAy
y
B
y
A
yy )000.100(
)000.100(
000.100)000.100(
1
+
=+
=
D, $!, *, ,*#,' 5",? 1 B A= (100.000 K =)
P/& ,P'' ,+,!' &$* 9'&$,* , A = ,*$&9,$*?
S = B 0 ,!+$!-,*? 1 B 100.000 #$ &$ +'!+$? 000.1001
=B
S = B 100.000 ,!+$!-,*? 1 B 100.000A , $!,? 000.1001
=A
C$!*,-",!+,,!+,
= yydy )000.100(
( )yLnyLny
dy
y
dy=+
000.100()(
000.100
1
000.100
1
000.100000.100
1
A& ,*$&9, !$* 5",' &' ,-"'-! , ,*+' '!,'?
( ) CtyLnyLn += 610*2000.100()(000.100
1
D$!, C ,* &' -$!*+'!+, , !+,'-!.
P/& 4D,*#,
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A& +$' ,& '!+&$'+$ *, +'!*$'?
tCt eCey
y 2,01
2,0 1
000.100==
+
P/& =#'' $%+,!, ,& 9'&$ HC , &' -$!*+'!+, , !+,'-!"*',$* ,& 9'&$ !-'& , &' -$!-! '' =(0)B 1.000 &",$
*"*++"$* = $%+,!,$*?
99
1
000.1000.100
000.11
0*2,0
1 ==
CeC
P/& 6 #'' $%+,!, &' *$&"-! #'+-"&' , &' ,-"'-!,,!-'& ,*#,
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Q ,* *"',!+, :+& #'' -'*$* ,! &$* 5", &' *$&"-! !$ #",,/'&&'*, #$ &$* +$$* -$!9,!-$!'&,* (-$$ *,#''-! ,9''%&,*). '= 9''-$!,* ,! ,& +$$ , R"!,"++' , -"'+$$,! #,$ ,& * "+&8'$ ,* ,& +$$ ,! ,& -"'& *, ,&, "!+''$ , #'*$ ?= "! !:,$ >$ , +,'-$!,* '.
P'' !",*+$ -'*$ ,*$&9, !"-',!+, "!' ,-"'-!,,!-'& , $,! "!$ -$! *" ,*#,-+9' -$!-! !-'&"*'!$ ,& +$$ , R"!, K "++' , -"'+$ $,! *, #$-,,
, &' *",!+, '!,'? L' ,-"'-! ' *"&'),( ytf
dt
dy=
-$! &'
-$!-! !-'& ( ) 00 yty =
E!+$!-,* ,& +$$ R4 #'' ,*+, #$%&,' ,*+ '$ #$ &'
*",!+, ,-"'-!?
D$!,?
A* ,& *",!+, 9'&$ ( Yn+1 ) ,* ,+,!'$ #$ ,& #,*,!+,9'&$ ( Yn ) * ,& #$"-+$ ,& +''$ ,& !+,9'&$ (/) #$ "!'#,!,!+, ,*+''. L' #,!,!+, ,* "! #$,$ #$!,'$ ,#,!,!+,* $!, K1 ,* &' #,!,!+, '& #!-#$ ,& !+,9'&$
K2 ,* &' #,!,!+, ,! ,& #"!+$ ,$ ,& !+,9'&$ "*'!$ K1
#'' ,+,!' ,& 9'&$ , HQ,! ,& #"!+$ xn+h
2"*'!$ ,&
+$$ , E"&,. K3 ,* $+' 9,8 &' #,!,!+, ,& #"!+$ ,$#,$ '/$' "*'!$ K2 #'' ,+,!' ,& 9'&$ , HQ K4 ,*&' #,!,!+, '& ;!'& ,& !+,9'&$ -$! ,& 9'&$ , HQ ,+,!'$#$ K3 .
7
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P$,'!$ &'* -"'+$ #,!,!+,* *, &, '*!' '=$ #,*$ ' &'*#,!,!+,* ,! ,& #"!+$ ,$?
S,!$ H/ ,& #'*$ -$,*#$!,!+, #'' -$!*," &' *$&"-!
!"-' ,! !",*+$ -'*$ ,& 9'&$ , / B 1.
L",$ ,,-+"'$* = -''$* +$'* &'* ,-"'-$!,* = $"&'*
*",!+,* ,! E>-,& #'' 5", !$* ",*+, &' ;-' 5", *,
$%+,! , &' *"&'-! , '-",$ ' &$* '+$* $%+,!$*?
L' ,-"'-! ,,!-'& ' ,*$&9, ,*?
( )yydt
dy= 000.10010*2 6
-$! &' -$!-! !-'&? =(0) B1.000.
E& +1 5",$ ,;!$ #$? K1=hf(x i ; y i)
( ) ( ) 261 000002,02,0000.10010*2;* nnnnnn yyyyytfhK ===
E& +2 5",$ ,;!$ #$? K2=f(x i+
1
2 h; y i+1
2 k1h)
))2/((*)))2/((000.100(10*2;* 11116
2221 kykyytfhK nn
Khn ++=++=
E& +, 5",$ ,;!$ #$? K3=f(x i+1
2h ; yi+
1
2k2h)
))2/((*)))2/((000.100(10*2;* 21216
2232 kykyytfhK nn
Khn ++=++=
E& +4 5",$ ,;!$ #$? K4=f(xi+h ; y i+k3h)
( ) )(*))(000.100(10*2;* 31316
34 kykykyhtfhK nnn ++=++=
E*+'* ,-"'-$!,* &'* "+&8'$* ,! E>-,& = -$!*,"$* &' *$&"-!!"-' , &' ,-"'-! #&'!+,'' -$! &' -$!-! !-'& ''.
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2.1 G';-' -$!*,"' -$! &$* 9'&$,* , *"&'-! #''&' #,' *"&'-! 60 '*.
N:,$ , I!9"$* I!,-+'$* ,! 60 '*
+ Q
F"' 1
T'%&' -$! &$* '+$* , &' #,' *"&'-!?
@ +1 +2 +, +4 '%' E&
0 1000.00000 1.00000 217.3440 21.2004 240.272 1000.00000 0.00000
1121.701
3 240.762264.2310
7 266.14022.6314
7121.704
1 0.002
2144.172
1 22.46320.342
4 323.723.001
0144.234
4 0.00623
3107.247
0 34.17643.063
7 32.34204430.241
4107.260
7 0.01126
421.71
7 430.0414471.06
0 474.727720.4144
421.62
3 0.0106
2672.3360
2 20.14446.273
73.0462.1726
2672.3631
0 0.0270
63244.741
7 627.01466.416
61.3276.331
03244.330
0 0.034
7
334.24
6 76.0176
2.33
31.7176
07.70
7
334.7
0 0.03
4764.60
0 07.16.2111
2 6.244010.4
24764.62
6 0.07307
7.741
10.4234
110.7
3611.2130
2123.044
07.460
4 0.0610
64.16
122.666
1403.03371
1412.3710
131.17
64.317 0.12611
11
34.3771
131.2762
167.67
1667.204
103.776
34.01 0.16130
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12
1001.762
103.00020
14.4717
16.6741
210.26477
1001.0 0.202
13
1171.3747
2107.64736
226.7213
2277.406
2443.70063
1171.624 0.207
14
14244.3100
2443.0613
2614.731
2626.6264
204.304
14244.61613 0.3023
1
1666.114
0
204.212
1
26.13
31
27.720
1
313.623
12
1666.47
7 0.364716
1.737
313.0064
336.2266
330.47220
367.7202
1.167 0.420
17
23233.764
367.17
371.730
3760.2
341.3231
23234.40 0.420
1
26.64347
341.046
4114.60
4121.407
426.42
260.13 0.636
1
31106.4244
426.0661
443.364
4443.403
42.41636
31107.036 0.6120
20
34.43271
42.1307
4704.04
4707.011
40.7213
346.071 0.66600
21
40247.341
40.707
42.0327
43.24043
42.7171
4024.4110 0.706
22
4136.636
42.6642
4.6042
4.7760
4.62
4137.42121 0.731
23
0121.26032
4.70
46.214
46.324
447.204
0122.0030 0.7431
24
103.4222
447.1016
4.16670
46.1160
400.4127
104.1612 0.7363
2
.2377
400.00
463.171
46.162
46.3123
.601 0.7223
26
64676.0760
46.2002
4424.6416
442.34
426.12
64677.20123 0.6363
27
6101.0622
4270.2701
40.04467
410.342
322.2302
6101.7423 0.6613
2
73201.063
323.411
3733.66740
3743.177
34.01100
73201.617 0.6127
2
763.61347
34.62221
331.132
3362.4724
3163.6023
763.1771 0.6624
30
02.1660
3164.40213
267.66304
20.1674
27.4773
02.712 0.16
31
326.46317
276.264
27.0074
2610.11133
242.31227
326.347 0.47170
32
73.760
2426.143
224.13233
2262.2463
201.26
74.14 0.4263
33
130.46767
202.1347
130.31
143.076
17.2213
130.110 0.3343
34
006.3462
17.02
1644.02
16.213
11.164
006.647 0.3431
3
171.624
11.621
131.06222
1401.167
121.07
171.631 0.302
36
3117.2242
121.023
1170.41
110.10
107.47727
3117.42 0.27140
37 423.6703 1076.143 0.2321 .2733 .322 423.62 0.233
27.171 .1
17.7126 2.2026
74.761
27.4104 0.21123
3
6101.6603 74.2122
67.230 66.36
621.7727
6101.7134 0.131
40
67.04 622.23240
63.1 6.31663
1.0410
67.67044 0.161
41
732.7647 1.43132
466.442 471.1437
42.7471
732.0601 0.14114
10
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42
722.17073 426.077
3.23706 3.16002
31.3317
722.2330 0.122
43
20.722 31.61643
317.61 320.307
2.20
20.742 0.10614
44
2.11 2.7744
261.14 264.33333
23.3074
2.6346 0.0166
4
72.10
73 23.0373
21.2007
0 217.4003
1.632
0
72.
67 0.0746
00.47 16.122
176.471 17.7743
161.01770
00.61663 0.0674
47
17.62620 161.146
14.222 146.14
132.2161
17.6436 0.016
4
333.016 132.3322
11.26660 120.740
10.12
333.146 0.0477
4
43.30 10.606 7.6 .2313 .011
44.02640 0.0420
0
2.16 .0640 0.2623 1.1376 73.00072
2.17 0.03623
1
633.3321 73.06467 6.012 66.26 .4743
633.36302 0.0304
2
6.71 .000 3.4427 4.3661 4.0234
6.62340 0.02621
3
73.1621 4.064 44.2004 44.62 40.164
73.346 0.0222
4
7.43310 40.23212 36.22432 36.62364 32.3424
7.41 0.016
34.1014 32.6346 2.67746 30.000 26.046
34.2611 0.016
6
64.747 27.00444 24.3104 24.763 22.10060
64.047 0.0130
7
.27600 22.1202 1.121 20.13320 1.1017
.2741 0.01140
0.323 1.117 16.3022 16.47 14.236
0.3300 0.0063
2.712 14.3 13.363 13.040 12.1412
2.76003 0.0012
60
3.20244 12.1212 10.331 11.06 .426
3.202 0.0064
2.2 G';-' #'' &' *,"!' *"&'-! ' 60 '* -$!-'%$ , 9''%&, ,! B 2x 107
11
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C$!+'3)$* #'' 60()'* -$! FB 2>10N7
+ Q
T'%&' -$! &$* '+$* , &' *,"!' *"&'-! 60 '* = -'%$, 9''%&, , &' -$!*+'!+, B 2>107
@ +1 +2 +, +4'%
' E&0 1000.00000 19.80000 19.99402 19.99592 20.19184 1000.00000 0.0000000
1 1019.99529 20.19183 20.38961 20.39154 20.59126 1019.99529 0.0000000
2 1040.38618 20.59124 20.79285 20.79482 20.99840 1040.38618 0.0000001
3 1061.18035 20.99839 21.20389 21.20590 21.41341 1061.18035 0.0000001
4 1082.38558 21.41340 21.62288 21.62492 21.83644 1082.38558 0.0000001
5 1104.00982 21.83643 22.04995 22.05204 22.26763 1104.00982 0.0000001
6 1126.06116 22.26762 22.48526 22.48738 22.70714 1126.06116 0.0000002
7 1148.54783 22.70712 22.92895 22.93112 23.15511 1148.54783 0.0000002
8 1171.47823 23.15509 23.38119 23.38340 23.61169 1171.47823 0.0000002
9 1194.86089 23.61168 23.84213 23.84437 24.07706 1194.86089 0.0000003
10 1218.70451 24.07704 24.31191 24.31421 24.55136 1218.70451 0.0000003
11 1243.01795 24.55134 24.79072 24.79305 25.03475 1243.01795 0.0000003
12 1267.81023 25.03474 25.27870 25.28108 25.52741 1267.81023 0.0000004
13 1293.09051 25.52739 25.77603 25.77845 26.02950 1293.09051 0.0000004
14 1318.86816 26.02948 26.28288 26.28534 26.54118 1318.86816 0.0000005
15 1345.15267 26.54117 26.79940 26.80191 27.06264 1345.15267 0.0000005
16 1371.95375 27.06262 27.32579 27.32835 27.59404 1371.95375 0.0000005
17 1399.28123 27.59403 27.86221 27.86481 28.13557 1399.28123 0.0000006
18 1427.14517 28.13555 28.40884 28.41149 28.68740 1427.14517 0.0000006
19 1455.55578 28.68739 28.96587 28.96857 29.24972 1455.55578 0.0000007
20 1484.52344 29.24971 29.53348 29.53623 29.82272 1484.52344 0.0000007
21 1514.05875 29.82270 30.11185 30.11466 30.40657 1514.05875 0.0000008
22 1544.17247 30.40656 30.70118 30.70404 31.00148 1544.17247 0.0000008
23 1574.87555 31.00146 31.30167 31.30457 31.60764 1574.87555 0.0000009
24 1606.17914 31.60762 31.91349 31.91645 32.22524 1606.17914 0.0000009
25 1638.09460 32.22522 32.53686 32.53988 32.85449 1638.09460 0.0000010
26 1670.63347 32.85447 33.17198 33.17505 33.49558 1670.63347 0.0000010
27 1703.80748 33.49556 33.81904 33.82217 34.14872 1703.80748 0.0000011
28 1737.62860 34.14870 34.47826 34.48144 34.81413 1737.62860 0.0000012
12
7/25/2019 Simulacion TP 2014_2 UNA
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29 1772.10897 34.81411 35.14985 35.15308 35.49200 1772.10897 0.0000012
30 1807.26097 35.49198 35.83401 35.83730 36.18256 1807.26097 0.0000013
31 1843.09716 36.18254 36.53096 36.53432 36.88603 1843.09716 0.0000014
32 1879.63035 36.88600 37.24093 37.24435 37.60261 1879.63035 0.0000014
33 1916.87355 37.60259 37.96413 37.96760 38.33254 1916.87355 0.0000015
34 1954.83998 38.33252 38.70078 38.70432 39.07604 1954.83998 0.0000016
35 1993.54311 39.07602 39.45112 39.45472 39.83334 1993.54311 0.0000017
36 2032.99662 39.83332 40.21537 40.21904 40.60467 2032.99662 0.0000017
37 2073.21442 40.60464 40.99377 40.99750 41.39026 2073.21442 0.0000018
38 2114.21066 41.39024 41.78655 41.79034 42.19035 2114.21066 0.0000019
39 2155.99972 42.19033 42.59395 42.59781 43.00518 2155.99973 0.0000020
40 2198.59623 43.00516 43.41621 43.42014 43.83500 2198.59623 0.0000021
41 2242.01504 43.83497 44.25357 44.25757 44.68004 2242.01504 0.0000022
42 2286.27125 44.68002 45.10629 45.11035 45.54056 2286.27126 0.0000023
43 2331.38023 45.54054 45.97461 45.97874 46.41681 2331.38023 0.0000024
44 2377.35757 46.41679 46.85878 46.86298 47.30904 2377.35758 0.0000025
45 2424.21913 47.30901 47.75906 47.76334 48.21751 2424.21913 0.0000026
46 2471.98102 48.21748 48.67570 48.68006 49.14247 2471.98102 0.0000027
47 2520.65959 49.14245 49.60898 49.61340 50.08420 2520.65960 0.0000028
48 2570.27150 50.08417 50.55914 50.56364 51.04295 2570.27150 0.0000029
49 2620.83361 51.04292 51.52646 51.53104 52.01899 2620.83361 0.0000030
50 2672.36310 52.01896 52.51121 52.51587 53.01259 2672.36310 0.0000031
51 2724.87738 53.01256 53.51365 53.51839 54.02402 2724.87738 0.0000033
52 2778.39415 54.02399 54.53406 54.53888 55.05356 2778.39416 0.0000034
53 2832.93139 55.05353 55.57272 55.57761 56.10148 2832.93139 0.0000035
54 2888.50734 56.10145 56.62990 56.63488 57.16807 2888.50734 0.0000036
55 2945.14051 57.16804 57.70588 57.71094 58.25361 2945.14052 0.0000038
56 3002.84973 58.25357 58.80095 58.80610 59.35837 3002.84973 0.0000039
57 3061.65407 59.35834 59.91540 59.92062 60.48265 3061.65407 0.0000040
58 3121.57291 60.48261 61.04950 61.05481 61.62673 3121.57291 0.0000042
59 3182.62590 61.62670 62.20355 62.20894 62.79091 3182.62591 0.0000043
60 3244.83300 62.79087 63.37783 63.38332 63.97547 3244.83300 0.0000045
2.3 V,;-'-! , &'* *"&'-$!,* *"&'-! ,-$!+'$* *"&+!,$* ,! ,& +,#$
13
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Contagiados simultaneos
ti funcion Yi
T'%&' -$! &$* 9'&$,* , &' *"&'-! , -$!+'$* *"&+!,$*
+ "!-! Q0 1000 1000.000000001 121.7041 121.7013332 144.2344 144.1721413 107.2607 107.2470334 21.623 21.7162 2672.3631 2672.336022316 3244.33 3244.74166337 334.7 334.246
4764.626 4764.6007 7.4604 7.741473310 64.317 64.1111 34.01 34.37712412 1001. 1001.7617713 1171.62 1171.37473314 14244.6161 14244.310601 1666.47 1666.11403316 1.166 1.7377017 23234.40 23233.76441 260.1 26.643467171 31107.037 31106.42442120 346.07 34.43271010
21 4024.411 40247.3413322 4137.4212 4136.63610623 0122.003 0121.2603240324 104.161 103.42222 .602 .2377426 64677.2012 64676.076003727 6101.7424 6101.06220742 73201.62 73201.06332 763.177 763.61347170
14
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30 02.713 02.167631 326.34 326.463166232 74.1 73.76030733 130.11 130.467667034 006.6 006.34623343 171.63 171.62433
36 3117.4 3117.22416337 423.6 423.6702733 27.410 27.17073 6101.713 6101.660344240 67.6704 67.0442141 732.06 732.76461042 722.233 722.1707266743 20.74 20.7220344 2.63 2.10604 72.7 72.1072646 00.6166 00.4710247 17.644 17.6261734 333.1 333.01642
4 44.0264 43.30020 2.1 2.101 633.363 633.332177362 6.6234 6.713 73.3 73.1621364 7.42 7.4330620 34.261 34.10142446 64.0 64.7473467 .274 .2760037 0.33 0.3237666 2.76 2.71173660 3.203 3.202437261 0.2233 0.217234
62 .2426 .237740163 66.622 66.624120464 72.67 72.67240176 77.6277 77.624761266 1.624 1.6772667 .0023 .00030026 7.7206 7.7116 .463 .44432170 1.76 1.76737271 3.2606 3.260372 4.421 4.413104373 .423 .41617074 6.3012 6.30062114
7 6.717 6.71174076 7.206 7.20163277 7.7 7.66477 .33 .337707117 .633 .63021300 . .71631 .07 .0762 .232 .23067413 .36 .34606
1
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4 .44 .431172 .01 .006446 .6644 .6643747 .723 .7221323 .771 .770220 .1 .103
0 .42 .412211 .766 .762602 . .033 .173 .1723404 .323 .322367 .44 .4416 .46 .476667 .62 .62103 .66 .6163 .71 .70700100 .76 .772
A';"// %&'%"/&'$/ #$ "&/ $/"#&/:
C$$ *, ,$*+ ,! &'* ;-'* = +'%&'* -$!+,!+9'* , &' '+'*"&'' '!+,$,!+, ,& +$$ !$* ,",*+' 5", ,& !:,$, !9"$* 9' ,! '",!+$ '& +'!*-" ,& +,#$.E! &' :&+' *"&'-! , &$* -$!+'$* *"&+!,$* #$,$*$%*,9' 5", '%'* ';-'* ,*+! *"#,#",*+'* &$ 5",,",*+' 5", E& +$$ , R"!, "++' ,* "! +$$%$!'$*$ #'' ,*$&9, ,*+, +#$ , *+"'-$!,* !"-'* #",*9,$* ,! &' +'%&' -$$ *, ,*+'%&8' ,! ,& +,#$ = ,& '",!+$ ,*,!$ '& #'*' , &$* 60 '* /'*+' &&,' ' &$* 100 '* = ,&'",!+$ ,* !*!;-'!+,.
3 OBJETI*O < MONTECARLO
E& $%,!$ , "! #'* *"',-'!$ ,*+ *,'!$ &'
-$!*+"--! , "!' ,#,*' &' -"'& *, "+&8'' #'' ,!,',!,' ,&-+-' = #'' ,& -$!+$& , "
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E& !9,& ,& ,%'&*, '& ;!'& , "! ,* ,*+ '$ #$?S ,& '"' ,! &' ,#,*' ,>-,, &' -'#'-' >' ,& '"'*$%'!+, *, %$+' ' +'9* ,& 9,+,,$ 5", ,* , "
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E+B E+1 A+K S+ $!, A+ -$,*#$!, '& '"' 5", &&,' ' &',#,*' = S+ '& '"' 5", *'&, , &' ,#,*' %,! *,' ,& '"' 5",*, 9,+, $ 5", *, *",&+' #'' ,!,' ,!,'.
E& #$-,,!+$ ,!,'& , *"&'-! #'' "! ,* -"'&5",' *,
#",, ,#,*,!+' #$ &$* *",!+,* #'*$*?
S, ,+,!' ,& '"' 5", &&,' ' &' ,#,*' A+ S, -'&-"&' ,& 9$&",! !-'& ,& ,%'&*, ','!$ ,&'"' 5", &&,'? E+ B E+1 A+ S ,& 9$&",! ,& ,%'&*, ,>-,, &' -'#'-' ,& *$*, -'&-"&' ,& '"' 5", *, 9,+, = ,& ,%'&*, 5",' ,! *"!9,& >$.
S E+J C'# V+B E+ C'#
E+B C'#
S, -'&-"&' &' ,'!' ,!*"'& #'' ,!,' ,!,' D+ S ,& !9,& ,& ,%'&*, ,* "'& $ *"#,$ ' &' ,'!' *,*'+*'-, +$' &' ,'!' = '& !9,& ,& ,%'&*, *, &, ,*+'&' ,'!'.
S E+ D+ DS+B D+
E+B E+ D+
S ,& !9,& ,& ,%'&*, ,* !,$ ' &' ,'!' *,*'+*'-, #'+, , &' ,'!' = '& !9,& ,& ,%'&*, *,/'-, "'& ' -,$.
S E+ D+ DS+ B E+
E+B 0
D$!, C'# ,#,*,!+' &' -'#'-' , &' ,#,*' V+ ,&9,+,!+$ ,! ,& ,* + = DS+ &' ,'!' *'+*,-/' ,! ,& ,* +.
P'' +,!' , ,*'$&&' ,& $,&$ *, ,5",, ,+,!'-$ *, ,!,' ,& '"' 5", &&,' '& ,%'&*, = &' ,'!' ,,!,'.
P'' -'&-"&' ,& '"' 5", &&,' '& ,%'&*, 5", ,* "! ,!,!$'&,'+$$ *, ,,-+:' ,'!+, &' '="' , &$* !:,$* '&,'+$$*.
1
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P'' ,&&$ *, ,!,' "! !:,$ '&,'+$$ A1 ,! E>-,& = &",$ *,/'-, "!' -$,*#$!,!-' ,!+, -/$ !:,$ = &'* #$%'%&',*,*#,-+9'* , 5", &&,", -,+' -'!+' , '"' '& ,%'&*,. E*,- ,& !:,$ '&,'+$$ A1 -$! "! '!$ , 9''-! , 0 '"!$ ,%, ,#,*,!+' &'* ,,!+,* #$*%&',* , &&,' '"' '&
,%'&*, -$! &$* 9'&$,* , 0 1 2 = 3. E& '!$ , 9''-! ,-,$ ' "!$ ,%, 9*, ,! 100 #'+,* = '*!'*, 20 ' &'#$*%&' , 5", !$ &&,", '"' ,! ,& ,* 20 ' &' #$*%&', 5", &&,", "!' "!' 30 ' &' #$*%&' , 5", &&,",! $*"!',* = ;!'&,!+, 30 ' &' #$*%&' , 5", &&,",! +,*"!',* , '"'. L' +'%&' *",!+, #,*,!+' "!' #$*%&,'*!'-! ,& !:,$ '&,'+$$ A1 ' &'* ,,!+,* -'!+',* ,'"' 5", #",,! &&,' '& ,%'&*,.
Valores del Nmero Aleatorio A10.2 0.2 0.3 0.320 40 70 100
A1 < 20 20
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I3$' 1
Mes
Emba
lse
Inicial (Et)
Aleatorio
A1
A1 *
100
Unida
des de
agua
ue
llegana la
re!res
a (At)
"#mero
de
unidades
derramadas !or
e$ceso
(%t)
Emb
alse
Intermedi
o (Et)
Aleat
orioA&
A& *
100
'emanda
!ara
generarenerga
('t)
'eman
da
dis!oni
bleCa!aci
dad
('t)
Embalse
al final
del mes(Et)
0 4 4
1 4 0.328 33 1 1 4 0.131 13 1 1 3
2 3 0.368 37 1 0 4 0.448 45 1 1 3
3 3 0.806 81 3 2 4 0.827 83 2 2 2
4 2 0.374 37 1 0 3 0.036 4 1 1 2
5 2 0.283 28 1 0 3 0.368 37 1 1 26 2 0.418 42 2 0 4 0.610 61 2 2 2
7 2 0.111 11 0 0 2 0.941 94 2 2 0
8 0 0.976 98 3 0 3 0.458 46 1 1 2
9 2 0.327 33 1 0 3 0.411 41 1 1 2
10 2 0.390 39 1 0 3 0.902 90 2 2 1
11 1 0.152 15 0 0 1 0.328 33 1 1 0
12 0 0.251 25 1 0 1 0.772 77 2 1 0
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13 0 0.592 59 2 0 2 0.084 8 1 1 1
14 1 0.819 82 3 0 4 0.981 98 2 2 2
15 2 0.865 87 3 1 4 0.969 97 2 2 2
16 2 0.144 14 0 0 2 0.102 10 1 1 1
17 1 0.975 98 3 0 4 0.670 67 2 2 2
18 2 0.628 63 2 0 4 0.304 30 1 1 3
19 3 0.883 88 3 2 4 0.537 54 2 2 2
20 2 0.319 32 1 0 3 0.022 2 1 1 2
21 2 0.832 83 3 1 4 0.899 90 2 2 2
22 2 0.570 57 2 0 4 0.432 43 1 1 3
23 3 0.012 1 0 0 3 0.580 58 2 2 1
24 1 0.541 54 2 0 3 0.585 59 2 2 1
25 1 0.432 43 2 0 3 0.969 97 2 2 1
26 1 0.412 41 2 0 3 0.736 74 2 2 1
27 1 0.133 13 0 0 1 0.451 45 1 1 0
28 0 0.633 63 2 0 2 0.868 87 2 2 0
29 0 0.317 32 1 0 1 0.945 95 2 1 0
30 0 0.570 57 2 0 2 0.729 73 2 2 0
Prom
edio
1+, 0-.&
1+0 0&// &/
0,0 1,
1,0 1,&
22
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4 CONCLUSIONES
E! ,& $%, "! '=$ !:,$ , $#,'-$!,* = 5", ,! -''#'*$ +$' ,& #$,$ #$!,'$ , -"'+$ #,!,!+,*.
E! ,*+, $%
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5 BIBLIOGRAFIA
U!9,*' N'-$!'& A%,+' (2006) I'$/%' #$ O5$%&'$/
II (,0). E&'%$'$ #$ G"+,,8 M. C''-'*./++#*?YY