-
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1/19
h h f(tn,yn)
0.1 0 10 -2 8
0.1 8 -1.6 6.4
0.2 6.4 -1.28 5.12
0.3 5.12 -1.024 4.096
0.4 4.096 -0.8192 3.2768
0.5 3.2768 -0.65536 2.62144
tn
yn
yn+1
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2/19
h
0.1 0 10 -2
0.1 8.2 -1.64
0.2 6.724 -1.3448
0.3 5.51368 -1.102736
0.4 4.5212176 -0.90424352
0.5 3.707398432 -0.7414796864
tn
yn
k1
-
7/23/2019 QUIZ 06 - 221 13 011
3/19
-1.6 8.2
-1.312 6.724
-1.07584 5.51368
-0.8821888 4.5212176
-0.723394816 3.707398432
-0.5931837491 3.0400667142
k2
yn+1
-
7/23/2019 QUIZ 06 - 221 13 011
4/19
h
0.1 0 10 -2
0.1 8.1873333333 -1.6374666667
0.2 6.7032427111 -1.3406485422
0.3 5.488168249 -1.09763364980.4 4.4933462844 -0.8986692569
0.5 3.6788523813 -0.7357704763
tn
yn
k1
-
7/23/2019 QUIZ 06 - 221 13 011
5/19
-1.8 -1.82 -1.636
-1.47372 -1.4900946667 -1.3394477333
-1.206583688 -1.2199901734 -1.0966505075
-0.9878702848 -0.9988466213 -0.8978643255-0.8088023312
-0.8177890238 -0.7351114521
-0.6621934286 -0.6695511334 -0.6018602496
k2
k3
k4
-
7/23/2019 QUIZ 06 - 221 13 011
6/19
8.1873333333
6.7032427111
5.488168249
4.49334628443.6788523813
3.0119990729
yn+1
-
7/23/2019 QUIZ 06 - 221 13 011
7/19
PREDIKTOR - KOREKTOR
h yn
0.1
0
1010
10
10
10
10
10
10
10
10
10
10
10
10
10
10
0.1
8.1818181818181808.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
8.181818181818180
6 694214876033060
tn
-
7/23/2019 QUIZ 06 - 221 13 011
8/19
0.2
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
6.694214876033060
0.3
5.4770848985725005.4770848985725005.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.4770848985725005.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
5.477084898572500
4.4812512806502304.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.4812512806502304.481251280650230
4 481251280650230
-
7/23/2019 QUIZ 06 - 221 13 011
9/19
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
0.5
3.6664783205320003.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.6664783205320003.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.6664783205320003.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
-
7/23/2019 QUIZ 06 - 221 13 011
10/19
f(xn,yn) yn(0)+1 f((x+1),yn(0)+1)
-20 8 -16.000000000000000
-20 8 -16.400000000000000
-20 8 -16.360000000000000
-20 8 -16.364000000000000
-20 8 -16.363600000000000
-20 8 -16.363640000000000
-20 8 -16.363636000000000
-20 8 -16.363636400000000
-20 8 -16.363636360000000
-20 8 -16.363636364000000
-20 8 -16.363636363600000
-20 8 -16.363636363640000
-20 8 -16.363636363636000
-20 8 -16.36363636363640000000
-20 8 -16.36363636363640000000
-20 8 -16.36363636363640000000
-16.363636364 6.5454545455 -13.09090909090910000000
-16.363636364 6.5454545455 -13.41818181818180000000
-16.363636364 6.5454545455 -13.38545454545450000000
-16.363636364 6.5454545455 -13.38872727272730000000
-16.363636364 6.5454545455 -13.38840000000000000000
-16.363636364 6.5454545455 -13.38843272727270000000
-16.363636364 6.5454545455 -13.38842945454550000000
-16.363636364 6.5454545455 -13.38842978181820000000
-16.363636364 6.5454545455 -13.38842974909090000000
-16.363636364 6.5454545455 -13.38842975236360000000
-16.363636364 6.5454545455 -13.38842975203640000000
-16.363636364 6.5454545455 -13.38842975206910000000
-16.363636364 6.5454545455 -13.38842975206580000000
-16.363636364 6.5454545455 -13.38842975206610000000
-16.363636364 6.5454545455 -13.38842975206610000000
-
7/23/2019 QUIZ 06 - 221 13 011
11/19
-13.388429752 5.3553719008 -10.97851239669420000000
-13.388429752 5.3553719008 -10.95173553719010000000
-13.388429752 5.3553719008 -10.95441322314050000000
-13.388429752 5.3553719008 -10.95414545454550000000
-13.388429752 5.3553719008 -10.95417223140500000000
-13.388429752 5.3553719008 -10.95416955371900000000
-13.388429752 5.3553719008 -10.95416982148760000000
-13.388429752 5.3553719008 -10.95416979471070000000
-13.388429752 5.3553719008 -10.95416979738840000000
-13.388429752 5.3553719008 -10.95416979712070000000
-13.388429752 5.3553719008 -10.95416979714740000000
-13.388429752 5.3553719008 -10.95416979714480000000
-13.388429752 5.3553719008 -10.95416979714500000000
-13.388429752 5.3553719008 -10.95416979714500000000
-10.954169797 4.3816679189 -8.76333583771600000000
-10.954169797 4.3816679189 -8.98241923365890000000-10.954169797
4.3816679189 -8.96051089406461000000
-10.954169797 4.3816679189 -8.96270172802404000000
-10.954169797 4.3816679189 -8.96248264462810000000
-10.954169797 4.3816679189 -8.96250455296769000000
-10.954169797 4.3816679189 -8.96250236213373000000
-10.954169797 4.3816679189 -8.96250258121713000000
-10.954169797 4.3816679189 -8.96250255930879000000
-10.954169797 4.3816679189 -8.96250256149962000000
-10.954169797 4.3816679189 -8.96250256128054000000
-10.954169797 4.3816679189 -8.96250256130245000000-10.954169797
4.3816679189 -8.96250256130026000000
-10.954169797 4.3816679189 -8.96250256130048000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-10.954169797 4.3816679189 -8.96250256130046000000
-8.9625025613 3.5850010245 -7.17000204904037000000
-8.9625025613 3.5850010245 -7.34925210026637000000
-8.9625025613 3.5850010245 -7.33132709514377000000
-8.9625025613 3.5850010245 -7.33311959565603000000
-8.9625025613 3.5850010245 -7.33294034560481000000
-8.9625025613 3.5850010245 -7.33295827060993000000
-8.9625025613 3.5850010245 -7.33295647810942000000
-8.9625025613 3.5850010245 -7.33295665735947000000-8.9625025613
3.5850010245 -7.33295663943447000000
8 9625025613 3 5850010245 7 33295664122697000000
-
7/23/2019 QUIZ 06 - 221 13 011
12/19
-8.9625025613 3.5850010245 -7.33295664104772000000
-8.9625025613 3.5850010245 -7.33295664106564000000
-8.9625025613 3.5850010245 -7.33295664106385000000
-8.9625025613 3.5850010245 -7.33295664106403000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-8.9625025613 3.5850010245 -7.33295664106401000000
-7.3329566411 2.9331826564 -5.86636531285121000000
-7.3329566411 2.9331826564 -6.01302444567249000000
-7.3329566411 2.9331826564 -5.99835853239036000000
-7.3329566411 2.9331826564 -5.99982512371857000000
-7.3329566411 2.9331826564 -5.99967846458575000000
-7.3329566411 2.9331826564 -5.99969313049903000000-7.3329566411
2.9331826564 -5.99969166390771000000
-7.3329566411 2.9331826564 -5.99969181056684000000
-7.3329566411 2.9331826564 -5.99969179590093000000
-7.3329566411 2.9331826564 -5.99969179736752000000
-7.3329566411 2.9331826564 -5.99969179722086000000
-7.3329566411 2.9331826564 -5.99969179723552000000
-7.3329566411 2.9331826564 -5.99969179723406000000
-7.3329566411 2.9331826564 -5.99969179723420000000
-7.3329566411 2.9331826564 -5.99969179723419000000
-7.3329566411 2.9331826564 -5.99969179723419000000-7.3329566411
2.9331826564 -5.99969179723419000000
-7.3329566411 2.9331826564 -5.99969179723419000000
-7.3329566411 2.9331826564 -5.99969179723419000000
-7.3329566411 2.9331826564 -5.99969179723419000000
-7.3329566411 2.9331826564 -5.99969179723419000000
-
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13/19
y(1)n+1
8.2000000000000
8.1800000000000
8.1820000000000
8.1818000000000
8.1818200000000
8.1818180000000
8.1818182000000
8.1818181800000
8.1818181820000
8.1818181818000
8.1818181818200
8.1818181818180
8.181818181818200
8.181818181818180 konvergen
8.181818181818180
8.181818181818180
6.709090909090910
6.692727272727270
6.694363636363640
6.694200000000000
6.694216363636360
6.694214727272730
6.694214890909090
6.694214874545450
6.694214876181820
6.694214876018180
6.694214876034550
6.694214876032910
6.694214876033070
6.694214876033060 konvergen
6.694214876033060
-
7/23/2019 QUIZ 06 - 221 13 011
14/19
5.475867768595040
5.477206611570250
5.477072727272730
5.477086115702480
5.477084776859500
5.477084910743800
5.477084897355370
5.477084898694220
5.477084898560330
5.477084898573720
5.477084898572380
5.477084898572510
5.477084898572500 konvergen
5.477084898572500
4.491209616829450
4.4802554470323104.481350864012020
4.481241322314050
4.481252276483850
4.481251181066870
4.481251290608570
4.481251279654400
4.481251280749810
4.481251280640270
4.481251280651230
4.4812512806501304.481251280650240
4.481251280650230 konvergen
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
4.481251280650230
3.674626050133190
3.665663547571890
3.666559797828020
3.666470172802400
3.666479135304970
3.666478239054710
3.666478328679730
3.6664783197172303.666478320613480
3 666478320523860
-
7/23/2019 QUIZ 06 - 221 13 011
15/19
3.666478320532820
3.666478320531920
3.666478320532010
3.666478320532000
3.666478320532010 konvergen
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.666478320532000
3.006512222836240
2.999179266195180
2.999912561859290
2.999839232292880
2.999846565249520
2.9998458319538502.999845905283420
2.999845897950460
2.999845898683760
2.999845898610430
2.999845898617760
2.999845898617030
2.999845898617100
2.999845898617090
2.999845898617090 konvergen
2.9998458986170902.999845898617090
2.999845898617090
2.999845898617090
2.999845898617090
2.999845898617090
-
7/23/2019 QUIZ 06 - 221 13 011
16/19
0 100.1 8.1873075308
0.2 6.7032004604
0.3 5.4881163609
0.4 4.4932896412
0.5 3.6787944117
tn
yn
-
7/23/2019 QUIZ 06 - 221 13 011
17/19
tn RK-1 RK-2 RK-4
0 10 10 10
0.1 8 8.200000000 8.187333333333
0.2 6.4 6.724000000 6.703242711111
0.3 5.12 5.513680000 5.488168249010
0.4 4.096 4.521217600 4.493346284406
0.5 3.2768 3.70738432 3.6788523812530
!O""E#T
dari tabel perbandingan nilai yn di atas,
dapat diketahui bahwa selisih nilai y(0,5) rungge kutta 4 dengan
y(0,5) analitik memiliki
maka dapat disimpulkan bahwa solusi Rungge kutta orde 4 lebih
teliti dibanding predikt
-
7/23/2019 QUIZ 06 - 221 13 011
18/19
TAB! "#BA$%&$'A$ $&!A& yn
PREDIKTOR-KOREKTOR $#$%ITIKRK1-$#$%ITIK
10 10 0.0000000000000
8.181818181818180 8.1873075308 0.1873075307798
6.694214876033060 6.7032004604 0.3032004603564
5.477084898572500 5.4881163609 0.3681163609403
4.481251280650230 4.4932896412 0.3972896411722
3.666478320532000 3.678744117 0.40144117144
selisih terkecil (tingkat eror paling kecil),
or korektor rungge-kutta orde 2 dan orde 1
-
7/23/2019 QUIZ 06 - 221 13 011
19/19
SYARIFAH AQLA
221 13 011
2/14/2014
&E%I&I'
RK2-$#$%ITIK RK4-$#$%ITIK PK-$#$%ITIK
0.000000000000 0.000000000000000000 0.0000000000000
0.012692469220 0.000025802553514254 0.0054893489616
0.020799539644 0.000042250754717088 0.0089855843233
0.025563639060 0.000051888070106365 0.0110314623678
0.027927958828 0.000056643234207954 0.0120383605220
0.028604020286 0.000057653855604 0.012316011824
&E%I&I' TERKE!I%
syariaha!la"gmail#com
mailto:[email protected]:[email protected]
