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: 3𝑥1 − 𝑥2 + 3𝑥3 = 2 5𝑥1 + 3𝑥2 + 𝑥3 = 6 𝑥1 + 2𝑥2 − 𝑥3 = 2 Jawab : 3 −1 3 𝑥1 2 𝑥 [5 3 1 ] [ 2 ] = [6] 1 2 −1 𝑥3 2 A x b Menggunakan matlab: clear; clc A = [3 -1 3; 5 3 1; 1 2 -1]; b = [2; 6; 2]; x = A\b x= 0.1429 1.4286 1.0000 2. Buat program matlab untuk menentukan nilai x yang menyebabkan nilai fungsi f(x)=0 𝑓(𝑥) = 𝑥 4 − 10 𝑥 3 + 35𝑥 2 − 50𝑥 + 24 Jawab: clear; clc p = [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: −3𝑥12 + 2 𝑥1 + 4𝑥2 = 5 2𝑥12 + 3 𝑥22 = 7 Jawab: 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 = [2 1]; options = optimset(‘Display’,’iter’); [x, fval] = fsolve(F,x0,options) FuncIteration count 0 3 1 6 2 9 3 10 4 13 5 14 6 15 7 18 8 21 Norm of step First-order f(x) optimality 202 855 16.655 0.919161 68 1.85289 0.587748 6.05 1.85289 0.8122 6.05 1.23404 0.20305 1.52 1.23404 0.20305 1.52 1.23404 0.0507625 1.52 1.22069 0.0126906 0.747 1.2161 0.0126906 0.741 Trust-region radius 1 1 2.3 2.3 0.203 0.203 0.0508 0.0127 0.0127 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 22 25 28 31 34 37 40 43 46 49 52 55 58 59 62 65 68 71 74 77 78 81 84 85 88 91 94 97 100 103 106 109 112 115 118 121 124 127 128 131 1.2161 1.21302 1.21239 1.21194 1.2115 1.2112 1.21087 1.21067 1.21043 1.2103 1.21011 1.21004 1.20989 1.20989 1.2095 1.20934 1.20924 1.20904 1.20892 1.20886 1.20886 1.20884 1.20884 1.20884 1.20883 1.20883 1.20883 1.20883 1.20883 1.20883 1.20883 1.20883 1.20883 1.20883 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 0.0126906 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.00317266 0.000793164 0.000793164 0.000793164 0.00198291 0.00198291 0.00198291 0.00198291 0.000495728 0.000495728 0.000495728 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 0.000123932 3.0983e-005 0.741 0.0127 0.177 0.00317 0.265 0.00317 0.297 0.00317 0.288 0.00317 0.309 0.00317 0.302 0.00317 0.317 0.00317 0.311 0.00317 0.323 0.00317 0.318 0.00317 0.327 0.00317 0.322 0.00317 0.322 0.00317 0.151 0.000793 0.0662 0.000793 0.0595 0.000793 0.0423 0.00198 0.0628 0.00198 0.0681 0.00198 0.0681 0.00198 0.0357 0.000496 0.0411 0.000496 0.0411 0.000496 0.0153 0.000124 0.00887 0.000124 0.013 0.000124 0.0112 0.000124 0.0129 0.000124 0.0119 0.000124 0.0129 0.000124 0.0122 0.000124 0.013 0.000124 0.0125 0.000124 0.0131 0.000124 0.0127 0.000124 0.0132 0.000124 0.0128 0.000124 0.0128 0.000124 0.00626 3.1e-005 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 134 137 140 143 144 147 150 151 154 157 160 163 166 169 172 175 178 181 184 187 190 193 196 199 202 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 1.20882 3.0983e-005 3.0983e-005 7.74575e-005 7.74575e-005 7.74575e-005 1.93644e-005 1.93644e-005 1.93644e-005 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 4.84109e-006 0.00211 0.00183 0.0023 0.00293 0.00293 0.00112 0.00162 0.00162 0.000623 0.000401 0.000336 0.000352 0.000423 0.000412 0.000456 0.000442 0.000477 0.000463 0.00049 0.000477 0.000499 0.000487 0.000505 0.000494 0.000509 3.1e-005 3.1e-005 7.75e-005 7.75e-005 7.75e-005 1.94e-005 1.94e-005 1.94e-005 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 4.84e-006 x= 0.2578 0.9193 fval = -1.0065 0.4426 4. Buat program matlab untuk menyelesaikan integrasi berikut ini: 0.4 ∫ 𝑥𝑒 −𝑥 𝑑𝑥 0 Jawab: clear; clc F = @(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: 𝑑𝑦 3𝑥 − + 2𝑥𝑦 = 0 𝑑𝑥 𝑦 dimana 𝑦(0) = 1.0 Jawab: 𝑑𝑦 3𝑥 = − 2𝑥𝑦 = 0 𝑑𝑥 𝑦 Menggunakan Matlab clear; clc xs=[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 𝑦(0) = 1,0 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: dy1 77.27 ( y 2 y1 y 2 y1 8.375 10 6 y12 ) dt dy2 ( y 3 y 2 y1 y 2 ) / 77.27 dt dy3 0.1610 ( y1 y 3 ) dt 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 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Dst 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.0143 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176 0.1176