Download - Tugas Komputasi Proses Kelompok 3 Ganjil
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Tugas Komputasi Proses
Kelompok 3 Ganjil
Anggota:
Mitha Alviyulita (090405019)
Torasman Sidabutar (100405019)
Ahmad Ridho (100405061)
Joko Mulia Pratama (110405021)
Yos Pawer Ambarita (110405035)
Fadhil Al Faruq Sinaga (120405049)
Kenrick (120405053)
Samsul Bahri Damanik (120405069)
Christin Natalia S (120405095)
Herlinawati Wici (120405099)
Fendi Suwito (120405123)
DEPARTEMEN TEKNIK KIMIA
FAKULTAS TEKNIK
UNIVERSITAS SUMATERA UTARA
MEDAN
2014
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1. Buat program matlab untuk menentukan nilai-nilai x1, x2, dan x3 dari sistem
persamaan linear berikut:
Penyelesaian:
%Ax=B
%x=A\B
clear;clc
A = [3 -1 3; 5 3 1; 1 2 -1];
B = [2; 6; 2];
x = A\B
Hasil Program:
x =
0.1429
1.4286
1.0000
2. Buat program Matlab untuk menentukan nilai x yang menyebabkan nilai fungsi
f(x)=0:
22
635
233
321
321
321
xxx
xxx
xxx
24503510)( 234 xxxxxf
bxA
2
6
2
121
135
313
3
2
1
x
x
x
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Penyelesaian:
clear;clc
p = [1 -10 35 -50 24];
x = roots(p)
Hasil Program:
x =
4.0000
3.0000
2.0000
1.0000
3. Buat program Matlab untuk menentukan nilai x1 dan x2 dari sistem persamaan
berikut:
Penyelesaian:
clear;clc
F = @(x)[-3*x(1).^2+2*x(1)+4*x(2)-5;2*x(1).^2+3*x(2).^2-7];
x0 = [4 4];
options = optimset('Display','iter');
[x,fval] = fsolve(F,x0,options)
Hasil program:
Norm of First-order Trust-region
Iteration Func-count f(x) step optimality radius
0 3 6170 1.81e+003 1
1 6 2544.31 1 918 1
732
5423
2
2
2
1
21
2
1
xx
xxx
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2 9 134.752 2.00934 131 2.5
3 12 5.04758 0.844305 16.2 5.02
4 15 0.111411 0.304491 1.66 5.02
5 18 0.000304865 0.069866 0.078 5.02
6 21 3.52974e-009 0.00407429 0.000264 5.02
7 24 4.87441e-019 1.39604e-005 3.1e-009 5.02
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
x =
0.8448 1.3629
fval =
1.0e-009 *
-0.5773
0.3926
Equation solved. The sum of squared function values, r = 4.874408e-019, is less than
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sqrt(options.TolFun) = 1.000000e-003. The relative norm of the gradient of r,
3.098578e-009,
is less than options.TolFun = 1.000000e-006.
Optimization Metric Options
relative norm(grad r) = 3.10e-009 TolFun = 1e-006 (default)
r = 4.87e-019 sqrt(TolFun) = 1.0e-003 (default)
4. Buat program Matlab untuk menyelesaikan integrasi berikut ini:
Penyelesaian:
clear;clc
F=@(x) x.*exp(-x);
%aturansimsons
Qs=quad(F,0,0.4)
%metodekuadratLobatto
Ql=quadl(F,0,0.4)
Hasil program:
Qs =
0.0616
Ql =
0.0616
4.0
0
dxxe x
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5. Buat program Matlab untuk menentukan nilai y(1) dari persamaan diferensial biasa
berikut:
Dimana y(0) = 1.0.
Penyelesaian:
clear;clc
xs = [0 5];
y0 = 1;
F = @(x,y)((3*x/y)-(2*x*y));
[x,y] = ode45(F,xs,y0)
plot(x,y(:,1),'-o')
Hasil Program:
x =
0
0.1250
0.2500
0.3750
0.5000
0.6250
0.7500
0.8750
1.0000
1.0810
1.1620
1.2429
1.3239
023
xyy
x
dx
dy
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1.4049
1.4859
1.5669
1.6479
1.7385
1.8292
1.9198
2.0105
2.1092
2.2079
2.3066
2.4053
2.4807
2.5562
2.6317
2.7072
2.7827
2.8581
2.9336
3.0091
3.0855
3.1618
3.2381
3.3145
3.3638
3.4130
3.4623
3.5115
3.5608
3.6101
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3.6593
3.7086
3.7691
3.8297
3.8902
3.9507
4.0019
4.0532
4.1044
4.1557
4.2069
4.2582
4.3094
4.3607
4.4110
4.4614
4.5117
4.5621
4.6068
4.6515
4.6962
4.7409
4.7801
4.8193
4.8586
4.8978
4.9233
4.9489
4.9744
5.0000
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y =
1.0000
1.0078
1.0290
1.0594
1.0940
1.1274
1.1566
1.1798
1.1968
1.2050
1.2112
1.2154
1.2184
1.2209
1.2224
1.2232
1.2236
1.2244
1.2247
1.2245
1.2244
1.2250
1.2252
1.2246
1.2243
1.2248
1.2250
1.2246
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1.2244
1.2249
1.2251
1.2246
1.2243
1.2255
1.2258
1.2244
1.2236
1.2244
1.2248
1.2246
1.2244
1.2247
1.2248
1.2247
1.2246
1.2249
1.2251
1.2247
1.2244
1.2249
1.2250
1.2247
1.2244
1.2250
1.2252
1.2246
1.2243
1.2252
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1.2255
1.2245
1.2239
1.2251
1.2255
1.2245
1.2239
1.2247
1.2251
1.2246
1.2242
1.2245
1.2246
1.2246
1.2247
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51
1.05
1.1
1.15
1.2
1.25
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6. Buat program Matlab untuk menentukan nilai-nilai y1, y2, dan y3 pada t = 1000 dari
sistem persamaan diferensial biasa berikut:
dimana y1(0) = 4.0, y2(0) = 1.1, dan y3(0) = 4.0.
Penyelesaian:
clear;clc
ts=[0 1000];
y0=[4 1.1 4];
F=@(t,y) [77.27*(y(2)-(y(1))*(y(2))+y(1)-(8.375*(10^(-6))*(y(1))^2)); ((y(3)-y(2)-
(y(1))*(y(2))))/(77.27); 0.1610*(y(1)-y(3))];
[t,y] = ode15s(F,ts,y0)
figure(1)
plot(t,y(:,1),'-o')
figure(2)
plot(t,y(:,2),'-o')
figure(3)
plot(t,y(:,3),'-o')
Hasil program:
t =
1.0e+003 *
0
0.0000
0.0000
)(1610.0
27.77/)(
)10375.8(27.77
31
3
21232
2
1
6
12121
yydt
dy
yyyydt
dy
yyyyydt
dy
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0.0000
0.0000
0.0001
0.0001
0.0001
0.0001
0.0002
0.0002
0.0003
0.0003
0.0004
0.0005
0.0005
0.0006
0.0006
0.0007
0.0008
0.0008
0.0008
0.0009
0.0009
0.0009
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
0.0011
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0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
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0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0012
0.0013
0.0013
0.0013
0.0013
0.0013
0.0013
0.0013
0.0014
0.0015
0.0016
0.0016
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0.0020
0.0023
0.0026
0.0029
0.0032
0.0033
0.0034
0.0035
0.0036
0.0037
0.0038
0.0038
0.0038
0.0038
0.0038
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
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0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
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0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0039
0.0040
0.0040
0.0040
0.0040
0.0040
0.0040
0.0040
0.0040
0.0041
0.0041
0.0041
0.0042
0.0042
0.0043
0.0044
0.0045
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0.0046
0.0049
0.0053
0.0056
0.0060
0.0066
0.0073
0.0079
0.0085
0.0098
0.0110
0.0122
0.0135
0.0147
0.0162
0.0178
0.0193
0.0208
0.0223
0.0239
0.0254
0.0270
0.0285
0.0300
0.0316
0.0331
0.0348
0.0364
0.0380
0.0397
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0.0413
0.0430
0.0448
0.0467
0.0486
0.0504
0.0523
0.0541
0.0560
0.0579
0.0598
0.0617
0.0635
0.0654
0.0674
0.0694
0.0713
0.0733
0.0753
0.0773
0.0796
0.0820
0.0844
0.0867
0.0891
0.0915
0.0946
0.0978
0.1010
0.1041
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0.1073
0.1126
0.1180
0.1233
0.1286
0.1362
0.1438
0.1513
0.1589
0.1665
0.1747
0.1830
0.1912
0.1995
0.2078
0.2174
0.2271
0.2367
0.2463
0.2560
0.2656
0.2656
0.2657
0.2657
0.2657
0.2657
0.2657
0.2657
0.2658
0.2658
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0.2659
0.2662
0.2666
0.2670
0.2704
0.2738
0.2773
0.2807
0.2856
0.2895
0.2925
0.2950
0.2969
0.2984
0.2995
0.3004
0.3011
0.3017
0.3021
0.3024
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0.3029
0.3031
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0.3036
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0.3037
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0.3041
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0.3042
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0.3068
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0.3069
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0.3080
0.3086
0.3092
0.3098
0.3104
0.3118
0.3131
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0.3159
0.3173
0.3188
0.3203
0.3219
0.3234
0.3249
0.3265
0.3280
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0.3296
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0.3327
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0.3363
0.3382
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0.3441
0.3460
0.3480
0.3499
0.3519
0.3538
0.3558
0.3578
0.3597
0.3617
0.3636
0.3656
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0.3687
0.3703
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0.3734
0.3750
0.3770
0.3790
0.3811
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0.3851
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0.3926
0.3944
0.3961
0.3978
0.4012
0.4045
0.4079
0.4113
0.4147
0.4213
0.4280
0.4347
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0.4480
0.4577
0.4674
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0.5995
0.6009
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![Page 33: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/33.jpg)
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![Page 34: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/34.jpg)
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![Page 35: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/35.jpg)
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![Page 36: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/36.jpg)
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![Page 37: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/37.jpg)
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![Page 38: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/38.jpg)
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![Page 39: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/39.jpg)
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0.6721
0.6728
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![Page 40: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/40.jpg)
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![Page 41: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/41.jpg)
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![Page 42: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/42.jpg)
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![Page 43: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/43.jpg)
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![Page 44: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/44.jpg)
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![Page 46: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/46.jpg)
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![Page 47: Tugas Komputasi Proses Kelompok 3 Ganjil](https://reader034.vdocuments.pub/reader034/viewer/2022050909/55cf9409550346f57b9f32ed/html5/thumbnails/47.jpg)
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y =
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0.8483 0.0000 0.2487
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0.0023 0.0001 0.3114
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0.0000 0.0000 0.0000
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0.0001 0.0000 0.0000
0.0001 0.0000 0.0000
0.0001 0.0000 0.0000
0.0001 0.0000 0.0000
0.0001 0.0000 0.0000
0.0001 0.0000 0.0000
0.0002 0.0000 0.0000
0.0002 0.0000 0.0000
0.0002 0.0000 0.0001
0.0002 0.0000 0.0001
0.0003 0.0000 0.0001
0.0004 0.0000 0.0001
0.0004 0.0000 0.0001
0.0005 0.0000 0.0001
0.0006 0.0000 0.0001
0.0008 0.0000 0.0001
0.0009 0.0000 0.0001
0.0011 0.0000 0.0001
0.0014 0.0000 0.0001
0.0017 0.0000 0.0001
0.0021 0.0000 0.0001
0.0026 0.0000 0.0001
0.0032 0.0000 0.0001
0.0041 0.0000 0.0001
0.0050 0.0000 0.0001
0.0063 0.0000 0.0001
0.0078 0.0000 0.0001
0.0100 0.0000 0.0001
0.0130 0.0000 0.0001
0.0163 0.0000 0.0002
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0.0209 0.0000 0.0002
0.0275 0.0000 0.0002
0.0350 0.0000 0.0002
0.0455 0.0000 0.0002
0.0601 0.0000 0.0003
0.0805 0.0000 0.0003
0.1090 0.0000 0.0004
0.1388 0.0000 0.0005
0.1493 0.0000 0.0005
0.1606 0.0000 0.0005
0.1728 0.0000 0.0006
0.1857 0.0000 0.0006
0.1994 0.0000 0.0006
0.2232 0.0000 0.0007
0.2492 0.0000 0.0008
0.2775 0.0000 0.0008
0.3079 0.0000 0.0009
0.3332 0.0000 0.0010
0.3597 0.0000 0.0011
0.3873 0.0000 0.0012
0.4161 0.0000 0.0012
0.4458 0.0000 0.0013
0.4800 0.0000 0.0015
0.5150 0.0000 0.0016
0.5506 0.0000 0.0017
0.5865 0.0000 0.0019
0.6225 0.0000 0.0020
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0.7946 0.0000 0.0029
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0.8558 0.0000 0.0033
0.9108 0.0000 0.0038
0.9591 0.0000 0.0042
1.0273 0.0000 0.0051
1.0773 0.0000 0.0060
1.1125 0.0000 0.0070
1.1366 0.0000 0.0080
1.1527 0.0000 0.0090
1.1686 0.0000 0.0108
1.1752 0.0000 0.0127
1.1777 0.0000 0.0146
1.1781 0.0000 0.0165
1.1772 0.0000 0.0183
1.1750 0.0000 0.0212
1.1722 0.0000 0.0240
1.1693 0.0000 0.0268
1.1664 0.0000 0.0296
1.1571 0.0000 0.0384
1.1477 0.0000 0.0471
1.1383 0.0000 0.0557
1.1290 0.0000 0.0641
1.0748 0.0000 0.1099
1.0201 0.0000 0.1513
0.9641 0.0000 0.1884
0.9062 0.0000 0.2214
0.8341 0.0000 0.2546
0.7518 0.0000 0.2822
0.7234 0.0000 0.2893
0.6913 0.0000 0.2959
0.6531 0.0000 0.3018
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0.6127 0.0000 0.3061
0.5738 0.0000 0.3088
0.5369 0.0000 0.3104
0.5002 0.0000 0.3113
0.4637 0.0000 0.3119
0.4258 0.0000 0.3123
0.3881 0.0000 0.3124
0.3493 0.0000 0.3125
0.3107 0.0000 0.3126
0.2722 0.0000 0.3125
0.2260 0.0000 0.3125
0.1877 0.0000 0.3124
0.1452 0.0000 0.3123
0.1090 0.0000 0.3122
0.0799 0.0000 0.3121
0.0531 0.0000 0.3119
0.0309 0.0000 0.3118
0.0183 0.0000 0.3117
0.0123 0.0000 0.3116
0.0086 0.0001 0.3116
0.0058 0.0001 0.3115
0.0037 0.0001 0.3115
0.0023 0.0001 0.3114
0.0014 0.0001 0.3114
0.0010 0.0001 0.3113
0.0008 0.0001 0.3113
0.0006 0.0001 0.3113
0.0004 0.0001 0.3112
0.0003 0.0001 0.3112
0.0002 0.0001 0.3111
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0.0001 0.0001 0.3111
0.0001 0.0001 0.3111
0.0001 0.0001 0.3110
0.0000 0.0001 0.3110
0.0000 0.0001 0.3110
0.0000 0.0001 0.3109
0.0000 0.0001 0.3109
0.0000 0.0001 0.3109
0.0000 0.0001 0.3109
0.0000 0.0001 0.3108
0.0000 0.0001 0.3108
0.0000 0.0001 0.3108
0.0000 0.0001 0.3107
0.0000 0.0001 0.3107
0.0000 0.0001 0.3107
0.0000 0.0001 0.3106
0.0000 0.0001 0.3106
0.0000 0.0001 0.3106
0.0000 0.0001 0.3105
0.0000 0.0001 0.3105
0.0000 0.0001 0.3104
0.0000 0.0001 0.3104
0.0000 0.0002 0.3103
0.0000 0.0002 0.3103
0.0000 0.0002 0.3102
0.0000 0.0002 0.3100
0.0000 0.0002 0.3099
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0.0000 0.0002 0.3092
0.0000 0.0003 0.3088
0.0000 0.0003 0.3084
0.0000 0.0003 0.3080
0.0000 0.0004 0.3077
0.0000 0.0004 0.3067
0.0000 0.0005 0.3057
0.0000 0.0006 0.3047
0.0000 0.0007 0.3038
0.0000 0.0008 0.3028
0.0000 0.0009 0.3008
0.0000 0.0011 0.2987
0.0000 0.0012 0.2967
0.0000 0.0014 0.2947
0.0000 0.0016 0.2927
0.0000 0.0019 0.2887
0.0000 0.0022 0.2849
0.0000 0.0025 0.2810
0.0000 0.0028 0.2773
0.0000 0.0035 0.2682
0.0000 0.0042 0.2595
0.0000 0.0048 0.2511
0.0000 0.0055 0.2429
0.0000 0.0072 0.2195
0.0000 0.0088 0.1983
0.0000 0.0102 0.1791
0.0000 0.0114 0.1618
0.0000 0.0125 0.1462
0.0000 0.0144 0.1155
0.0000 0.0158 0.0913
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0.0000 0.0167 0.0722
0.0000 0.0173 0.0570
0.0000 0.0176 0.0451
0.0000 0.0177 0.0352
0.0000 0.0176 0.0275
0.0000 0.0174 0.0215
0.0000 0.0171 0.0168
0.0000 0.0167 0.0132
0.0000 0.0163 0.0102
0.0000 0.0158 0.0079
0.0000 0.0153 0.0061
0.0000 0.0148 0.0048
0.0000 0.0143 0.0037
0.0000 0.0138 0.0029
0.0000 0.0132 0.0021
0.0000 0.0126 0.0015
0.0000 0.0120 0.0011
0.0000 0.0114 0.0008
0.0000 0.0109 0.0006
0.0000 0.0103 0.0004
0.0000 0.0098 0.0003
0.0000 0.0094 0.0002
0.0000 0.0089 0.0002
0.0000 0.0085 0.0001
0.0000 0.0080 0.0001
0.0000 0.0076 0.0001
0.0000 0.0073 0.0001
0.0000 0.0069 0.0000
0.0000 0.0066 0.0000
0.0000 0.0062 0.0000
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0.0000 0.0059 0.0000
0.0000 0.0057 0.0000
0.0000 0.0055 0.0000
0.0000 0.0053 0.0000
0.0000 0.0051 0.0000
0.0000 0.0049 0.0000
0.0000 0.0047 0.0000
0.0000 0.0046 0.0000
0.0000 0.0043 0.0000
0.0000 0.0041 0.0000
0.0000 0.0039 0.0000
0.0000 0.0037 0.0000
0.0000 0.0035 0.0000
0.0000 0.0032 0.0000
0.0000 0.0031 0.0000
Figure 1
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Figure 2
Figure 3
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400
600
800
1000
1200
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0 100 200 300 400 500 600 700 800 900 10000
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