Quiz Komputasi Proses

Kelompok IV Ganjil

Anggota : 1. David Makmur (090405043) 2. M. Fauzy Ramadhan Tarigan (110405091) 3. Rizka Rinda Pramasti (110405063) 4. Rio Agung Prakoso (110405015) 5. Rismadhani Elita (120405013) 6. Nisaul Fadilah (120405101) 7. Marfuah Lubis (120405103) 8. Lara Indra Ranita (120405009) 9. Alvian (120405031)10. Andhika Setiawan (120405015)

1. Buat program matlab untuk menentukan nilai-nilai x1, x2, dan x3 dari sistem persamaan liniear berikut:

3 x1−x2+3 x3=2

5 x1+3 x2+x3=6

x1+2x2−x3=2

Jawab :

[3 −1 35 3 11 2 −1][ x1

x2

x3]=[262]

Menggunakan matlab:clear; clcA = [3 -1 3; 5 3 1; 1 2 -1];b = [2; 6; 2];x = A\b

x =

0.1429 1.4286 1.0000

A x b

2. Buat program matlab untuk menentukan nilai x yang menyebabkan nilai fungsi f(x)=0

f ( x )=x 4−10 x3+35x2−50 x+24

Jawab:

clear; clcp = [1 -10 35 -50 24];x = roots(p)

x =

4.0000 3.0000 2.0000 1.0000

3. Buat program matlab untuk menentukan nilai x1 dan x2 dari sistem persamaan berikut:

−3 x12+2x1+4 x2=5

2 x12+3 x2

2=7

Jawab:

clear; clcF = @(x)[-3*x(1).^2 + 2*x(1) + 4*x(2) -5; 2*x(1).^2 + 3*x(2).^2 – 7];x0 = [2 1];options = optimset(‘Display’,’iter’);

[x, fval] = fsolve(F,x0,options)

Func- Norm of First-order Trust-region Iteration count f(x) step optimality radius 0 3 202 855 1 1 6 16.655 0.919161 68 1 2 9 1.85289 0.587748 6.05 2.3 3 10 1.85289 0.8122 6.05 2.3 4 13 1.23404 0.20305 1.52 0.203 5 14 1.23404 0.20305 1.52 0.203 6 15 1.23404 0.0507625 1.52 0.0508 7 18 1.22069 0.0126906 0.747 0.0127

8 21 1.2161 0.0126906 0.741 0.0127 9 22 1.2161 0.0126906 0.741 0.0127 10 25 1.21302 0.00317266 0.177 0.00317 11 28 1.21239 0.00317266 0.265 0.00317 12 31 1.21194 0.00317266 0.297 0.00317 13 34 1.2115 0.00317266 0.288 0.00317 14 37 1.2112 0.00317266 0.309 0.00317 15 40 1.21087 0.00317266 0.302 0.00317 16 43 1.21067 0.00317266 0.317 0.00317 17 46 1.21043 0.00317266 0.311 0.00317 18 49 1.2103 0.00317266 0.323 0.00317 19 52 1.21011 0.00317266 0.318 0.00317 20 55 1.21004 0.00317266 0.327 0.00317 21 58 1.20989 0.00317266 0.322 0.00317 22 59 1.20989 0.00317266 0.322 0.00317 23 62 1.2095 0.000793164 0.151 0.000793 24 65 1.20934 0.000793164 0.0662 0.000793 25 68 1.20924 0.000793164 0.0595 0.000793 26 71 1.20904 0.00198291 0.0423 0.00198 27 74 1.20892 0.00198291 0.0628 0.00198 28 77 1.20886 0.00198291 0.0681 0.00198 29 78 1.20886 0.00198291 0.0681 0.00198 30 81 1.20884 0.000495728 0.0357 0.000496 31 84 1.20884 0.000495728 0.0411 0.000496 32 85 1.20884 0.000495728 0.0411 0.000496 33 88 1.20883 0.000123932 0.0153 0.000124 34 91 1.20883 0.000123932 0.00887 0.000124 35 94 1.20883 0.000123932 0.013 0.000124 36 97 1.20883 0.000123932 0.0112 0.000124 37 100 1.20883 0.000123932 0.0129 0.000124 38 103 1.20883 0.000123932 0.0119 0.000124 39 106 1.20883 0.000123932 0.0129 0.000124 40 109 1.20883 0.000123932 0.0122 0.000124 41 112 1.20883 0.000123932 0.013 0.000124 42 115 1.20883 0.000123932 0.0125 0.000124 43 118 1.20882 0.000123932 0.0131 0.000124 44 121 1.20882 0.000123932 0.0127 0.000124 45 124 1.20882 0.000123932 0.0132 0.000124 46 127 1.20882 0.000123932 0.0128 0.000124 47 128 1.20882 0.000123932 0.0128 0.000124 48 131 1.20882 3.0983e-005 0.00626 3.1e-005

49 134 1.20882 3.0983e-005 0.00211 3.1e-005 50 137 1.20882 3.0983e-005 0.00183 3.1e-005 51 140 1.20882 7.74575e-005 0.0023 7.75e-005 52 143 1.20882 7.74575e-005 0.00293 7.75e-005 53 144 1.20882 7.74575e-005 0.00293 7.75e-005 54 147 1.20882 1.93644e-005 0.00112 1.94e-005 55 150 1.20882 1.93644e-005 0.00162 1.94e-005 56 151 1.20882 1.93644e-005 0.00162 1.94e-005 57 154 1.20882 4.84109e-006 0.000623 4.84e-006 58 157 1.20882 4.84109e-006 0.000401 4.84e-006 59 160 1.20882 4.84109e-006 0.000336 4.84e-006 60 163 1.20882 4.84109e-006 0.000352 4.84e-006 61 166 1.20882 4.84109e-006 0.000423 4.84e-006 62 169 1.20882 4.84109e-006 0.000412 4.84e-006 63 172 1.20882 4.84109e-006 0.000456 4.84e-006 64 175 1.20882 4.84109e-006 0.000442 4.84e-006 65 178 1.20882 4.84109e-006 0.000477 4.84e-006 66 181 1.20882 4.84109e-006 0.000463 4.84e-006 67 184 1.20882 4.84109e-006 0.00049 4.84e-006 68 187 1.20882 4.84109e-006 0.000477 4.84e-006 69 190 1.20882 4.84109e-006 0.000499 4.84e-006 70 193 1.20882 4.84109e-006 0.000487 4.84e-006 71 196 1.20882 4.84109e-006 0.000505 4.84e-006 72 199 1.20882 4.84109e-006 0.000494 4.84e-006 73 202 1.20882 4.84109e-006 0.000509 4.84e-006

x =

0.2578 0.9193

fval =

-1.0065 0.4426

4. Buat program matlab untuk menyelesaikan integrasi berikut ini:

∫0

0.4

xe− xdx

Jawab:

clear; clcF = @(x)x.*exp(-x);Qs=quad(F,0,0.4)Ql=quadl(F,0,0.4)

Qs =

0.0616

Ql =

0.0616

5. Buat program matlab untuk menentukan nilai y(1) dari persamaan diferensial biasa berikut:

dydx

−3 xy

+2xy=0

dimana y (0 )=1.0

Jawab:dydx

=3 xy

−2 xy=0 y (0 )=1,0

Menggunakan Matlabclear; clcxs=[0 10];y0=1;F=@(x,y)(3*x/y-2*x*y);[X,Y]=ode45(F,xs,y0);plot(X,Y(:,1),’-o’)

X =

0 0.0849 0.1698 0.2547

0.3396 0.4245 0.5094 0.5943 0.6792 0.7774 0.8757 0.9739 1.0721 1.1704 1.2686 1.3669 1.4651 1.5503 1.6354 1.7206 1.8057 1.8958 1.9859 2.0760 2.1661 2.2654 2.3647 2.4640 2.5632 2.6303 2.6974 2.7644 2.8315 2.8985 2.9656 3.0327 3.0997 3.1749 3.2501 3.3253 3.4004 3.4519 3.5033 3.5548 3.6062

3.6577 3.7091 3.7605 3.8120 3.8715 3.9311 3.9906 4.0501 4.0976 4.1451 4.1926 4.2401 4.2876 4.3351 4.3827 4.4302 4.4800 4.5298 4.5796 4.6295 4.6766 4.7236 4.7707 4.8178 4.8584 4.8990 4.9396 4.9802 5.0167 5.0532 5.0897 5.1262 5.1637 5.2011 5.2386 5.2761 5.3172 5.3583 5.3994 5.4405 5.4824

5.5243 5.5661 5.6080 5.6453 5.6825 5.7197 5.7570 5.7890 5.8211 5.8531 5.8851 5.9162 5.9472 5.9783 6.0093 6.0436 6.0779 6.1122 6.1464 6.1839 6.2213 6.2588 6.2962 6.3318 6.3673 6.4028 6.4383 6.4685 6.4986 6.5287 6.5589 6.5860 6.6131 6.6403 6.6674 6.6962 6.7250 6.7538 6.7827 6.8155 6.8484

6.8813 6.9142 6.9481 6.9821 7.0160 7.0500 7.0797 7.1095 7.1392 7.1689 7.1941 7.2193 7.2445 7.2697 7.2945 7.3192 7.3440 7.3688 7.3971 7.4254 7.4537 7.4820 7.5136 7.5453 7.5769 7.6086 7.6384 7.6682 7.6981 7.7279 7.7527 7.7775 7.8023 7.8271 7.8494 7.8717 7.8939 7.9162 7.9404 7.9646 7.9888

8.0130 8.0414 8.0698 8.0982 8.1266 8.1561 8.1856 8.2151 8.2446 8.2701 8.2955 8.3209 8.3463 8.3676 8.3888 8.4100 8.4313 8.4524 8.4735 8.4945 8.5156 8.5403 8.5650 8.5897 8.6144 8.6425 8.6705 8.6985 8.7266 8.7529 8.7792 8.8055 8.8318 8.8533 8.8747 8.8962 8.9177 8.9369 8.9561 8.9753 8.9945

9.0158 9.0371 9.0583 9.0796 9.1050 9.1304 9.1557 9.1811 9.2077 9.2342 9.2607 9.2872 9.3098 9.3324 9.3549 9.3775 9.3962 9.4148 9.4334 9.4521 9.4707 9.4893 9.5080 9.5266 9.5488 9.5709 9.5931 9.6153 9.6408 9.6662 9.6917 9.7172 9.7410 9.7648 9.7886 9.8124 9.8316 9.8508 9.8700 9.8892 9.9063

9.9235 9.9406 9.9577 9.9683 9.9788 9.9894 10.0000

Y =

1.0000 1.0036 1.0139 1.0300 1.0502 1.0730 1.0965 1.1195 1.1407 1.1624 1.1802 1.1938 1.2039 1.2120 1.2174 1.2198 1.2212 1.2228 1.2238 1.2240 1.2241 1.2246 1.2249 1.2246 1.2245 1.2251 1.2254 1.2245 1.2241 1.2246

1.2249 1.2246 1.2244 1.2248 1.2249 1.2247 1.2245 1.2252 1.2254 1.2245 1.2240 1.2246 1.2249 1.2246 1.2244 1.2248 1.2249 1.2247 1.2245 1.2250 1.2252 1.2246 1.2243 1.2248 1.2250 1.2246 1.2244 1.2249 1.2250 1.2247 1.2244 1.2251 1.2253 1.2246 1.2241 1.2252 1.2256 1.2245 1.2238 1.2249 1.2253

1.2245 1.2240 1.2247 1.2250 1.2246 1.2244 1.2248 1.2250 1.2247 1.2245 1.2250 1.2251 1.2246 1.2243 1.2252 1.2255 1.2245 1.2239 1.2251 1.2256 1.2245 1.2238 1.2247 1.2251 1.2246 1.2242 1.2247 1.2249 1.2247 1.2245 1.2249 1.2250 1.2247 1.2245 1.2251 1.2253 1.2246 1.2242 1.2253 1.2257 1.2245

1.2237 1.2249 1.2253 1.2245 1.2240 1.2246 1.2249 1.2246 1.2244 1.2248 1.2249 1.2247 1.2245 1.2250 1.2251 1.2246 1.2244 1.2253 1.2256 1.2245 1.2239 1.2252 1.2256 1.2245 1.2237 1.2246 1.2250 1.2246 1.2243 1.2247 1.2249 1.2247 1.2245 1.2248 1.2250 1.2247 1.2245 1.2251 1.2253 1.2246 1.2241

1.2254 1.2258 1.2244 1.2236 1.2248 1.2253 1.2245 1.2240 1.2246 1.2249 1.2246 1.2244 1.2248 1.2249 1.2247 1.2245 1.2250 1.2251 1.2246 1.2244 1.2254 1.2257 1.2245 1.2238 1.2252 1.2257 1.2245 1.2237 1.2246 1.2250 1.2246 1.2243 1.2247 1.2248 1.2247 1.2245 1.2248 1.2250 1.2247 1.2245 1.2252

1.2254 1.2246 1.2241 1.2255 1.2259 1.2244 1.2235 1.2248 1.2253 1.2245 1.2240 1.2246 1.2248 1.2246 1.2245 1.2248 1.2249 1.2247 1.2246 1.2250 1.2251 1.2246 1.2244 1.2254 1.2258 1.2245 1.2237 1.2252 1.2258 1.2244 1.2236 1.2245 1.2249 1.2246 1.2243 1.2247 1.2248 1.2247 1.2246 1.2248 1.2249

1.2247 1.2245 1.2252 1.2254 1.2246 1.2241 1.2255 1.2260 1.2244 1.2234 1.2247 1.2253 1.2245 1.2240 1.2245 1.2248 1.2246 1.2245 1.2246 1.2246 1.2247 1.2247

6. Buat program matlab untuk menentukan nilai-nilai y1, y2, dan y3 pada t= 1000 dari sistem persamaan diferensial biasa berikut:

)(1610.0

27.77/)(

)10375.8(27.77

313

21232

21

61212

1

yydt

dy

yyyydt

dy

yyyyydt

dy

dimana y1(0) = 4.0, y2(0) = 1.1, dan y3(0) = 4.0

Jawab: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]=ode45(F,ts,y0)figure(1)

plot(t,y(:,1),’-o’)figure(2)plot(t,y(:,2),’-o’)figure(3)plot(t,y(:,3),’-o’)

0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1177 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176

0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 0.0000 0.0143 0.1176 Dst