Bab 7 - Contoh Metode Runge-Kutta Orde 2

Embed Size (px)

DESCRIPTION

Metoda Numerik

Citation preview

  • yn+1 = yn + (k1 + k2) dengany(0) = 1 h = 0.1 k1 = hf (xn, yn)

    k2 = hf (xn+h, yn+k1)

    x k1 k2

    0 1 -0.1000 -0.1011 -0.1006 0.89940.1 0.8994 -0.1012 -0.1053 -0.1032 0.79620.2 0.7962 -0.1056 -0.1148 -0.1102 0.68600.3 0.6860 -0.1158 -0.1354 -0.1256 0.56050.4 0.5605 -0.1384 -0.1869 -0.1627 0.39780.5 0.3978 -0.2014 -0.4492 -0.3253 0.07250.6 0.0725 -1.3201 0.1502 -0.5850 -0.51250.7 -0.5125 0.2651 0.4842 0.3747 -0.13780.8 -0.1378 0.8056 -0.0598 0.3729 0.23510.9 0.2351 -0.3354 1.0970 0.3808 0.61591 0.6159 -0.0624 -0.0707 -0.0665 0.5494

    1.1 0.5494 -0.0720 -0.0895 -0.0807 0.46871.2 0.4687 -0.0934 -0.1365 -0.1149 0.35371.3 0.3537 -0.1527 -0.3574 -0.2550 0.09871.4 0.0987 -0.8732 0.2791 -0.2971 -0.19841.5 -0.1984 0.6541 -0.0594 0.2973 0.09901.6 0.0990 -0.8503 0.3031 -0.2736 -0.17461.7 -0.1746 0.7427 0.0040 0.3733 0.19871.8 0.1987 -0.3233 0.9927 0.3347 0.53341.9 0.5334 0.0025 0.0134 0.0080 0.54142 0.5414 0.0153 0.0304 0.0228 0.5642

    2.1 0.5642 0.0328 0.0525 0.0426 0.60692.2 0.6069 0.0552 0.0790 0.0671 0.67402.3 0.6740 0.0816 0.1077 0.0946 0.76862.4 0.7686 0.1099 0.1362 0.1230 0.89162.5 0.8916 0.1378 0.1629 0.1504 1.04202.6 1.0420 0.1640 0.1871 0.1756 1.21752.7 1.2175 0.1879 0.2088 0.1984 1.41592.8 1.4159 0.2094 0.2285 0.2189 1.63482.9 1.6348 0.2288 0.2463 0.2376 1.87243 1.8724 0.2466 0.2628 0.2547 2.1271

    3.1 2.1271 0.2630 0.2782 0.2706 2.3977

    yn y yn+1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.6-0.4-0.2

    00.20.40.60.8

    11.2

    y '=x 1y

  • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.6-0.4-0.2

    00.20.40.60.8

    11.2

  • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.6

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    xn

    yn

  • n = Iterasi 0 1 2 3 4 5

    tn 0 0.1 0.2 0.3 0.4 0.5 0.6xn 1 1.0025 1.0099 1.0219 1.0382 1.0582yn 0 0.0497 0.0977 0.1424 0.1824 0.2167k1 0 0.005 0.0098 0.0142 0.0182 0.0217l1 0.05 0.0491 0.0466 0.0426 0.0373 0.0312k2 0.0025 0.0074 0.0121 0.0164 0.0201 0.0232l2 0.0498 0.048 0.0447 0.04 0.0343 0.0279k3 0.0025 0.0074 0.012 0.0162 0.02 0.0231l3 0.0498 0.0481 0.0448 0.0401 0.0345 0.0281k4 0.005 0.0098 0.0142 0.0183 0.0217 0.0245l4 0.0491 0.0466 0.0425 0.0373 0.0312 0.0247

    xn + 1 = C 1.0025 1.0099 1.0219 1.0382 1.0582 1.0813yn + 1 = C' 0.0497 0.0977 0.1424 0.1824 0.2167 0.2447

  • 0.7 0.8 0.9 1

    PDB Orde 1Chart PDB Orde 1PDB Orde 2