METODE NUMERIK
“METODE ITERASI GAUSS-SEIDEL DAN
DIFERENSIASI NUMERIK”
Nama
: Rian Adi Wirawan
NIM
: 21060112130134
Kelas
: C
JURUSAN TEKNIK ELEKTRO
FAKULTAS TEKNIK
METODE ITERASI GAUSS-SEIDEL
PR :
x+y+2z=9
2x+4y−3z=1
3x+6y−5z=0
Misalkan :
x=9−y−2z
y=1−2x+3z 4
z=3x+6y 5
Inisialisasi :
y=1; z=1
Iterasi x y z error x error y error z
0 1 1
1 6 -2 1.2 -1.5 0.1
2 8.6 -3.15 1.38 1.3 -0.575 0.09
3 9.39 -3.41 1.542 0.395 -0.13 0.081
4 9.326 -3.2565 1.6878 -0.032 0.07675 0.0729
5 8.8809 -2.9246 1.81902
-0.22255 0.16595 0.06561
6 8.28656
-2.52902
1.93711 8
-0.29717
0.19779 3
0.05904 9
7 7.654779 2.12455- 2.043406 0.31589- 0.202232 0.053144
8 7.037739 1.73631- 2.139066 0.30852- 0.194118 0.04783
9
6.45818 3
-1.37479
2.22515 9
-0.28978
0.18076 1
0.04304 7
10
5.92447 5
-1.04337
2.30264 3
-0.26685
0.16571 2
11 5.438082 0.74206- 2.372379 -0.2432 0.150655 0.034868
12 4.997301 0.46937- 2.435141 0.22039- 0.136346 0.031381
13
4.59908 5
-0.22319
2.49162 7
-0.19911 0.12309
0.02824 3
14
4.23993 3
-0.00125
2.54246 4
-0.17958 0.11097
0.02541 9
15
3.91631 8
0.19868 9
2.58821 8
-0.16181
0.09996 8
0.02287 7
16
3.62487 5
0.37872 6
2.62939 6
-0.14572
0.09001 8
0.02058 9
17 3.362482 0.540806 2.666456 -0.1312 0.08104 0.01853
18 3.126282 0.686702 2.699811 -0.1181 0.072948 0.016677
19
2.91367
7 0.81802 2.72983 -0.1063
0.06565 9
0.01500 9
20
2.72232 1
0.93621 2
2.75684 7
-0.09568
0.05909 6
0.01350 9
21
2.55009 5
1.04258 8
2.78116 2
-0.08611
0.05318 8
0.01215 8
22
2.39508 8
1.13832 7
2.80304
6 -0.0775 0.04787
0.01094 2
23
2.25558 1
1.22449 4
2.82274 1
-0.06975
0.04308 3
0.00984 8
24 2.130024 1.302044 2.840467 0.06278- 0.038775 0.008863
25 2.017022 1.371839 2.85642 -0.0565 0.034898 0.007977
26 1.91532
1.43465 5
2.87077 8
-0.05085
0.03140 8
0.00717 9
27
1.82378
8 1.49119
2.88370 1
-0.04577
0.02826 7
0.00646 1
28
1.74140 9
1.54207
1 2.89533
-0.04119 0.02544
0.00581 5
29
1.66726 8
1.58786 4
2.90579 7
-0.03707
0.02289 6
0.00523 3
30
1.60054 1
1.62907 7
2.91521 8
-0.03336
0.02060
7 0.00471
31 1.540487 1.66617 2.923696 0.03003- 0.018546 0.004239
5 7 4 0.02432 2 4
34
1.39401 5
1.75663 8
2.94437 4
-0.02189 0.01352 0.00309
35
1.35461 4
1.78097 4
2.94993
7 -0.0197
0.01216 8
0.00278 1
36
1.31915 2
1.80287 7
2.95494 3
-0.01773
0.01095 1
0.00250 3
37 1.287237 1.822589 2.959449 0.01596- 0.009856 0.002253
38 1.258513 1.84033 2.963504 0.01436- 0.008871 0.002028
39
1.23266 2
1.85629 7
2.96715 4
-0.01293
0.00798 4
0.00182 5
40
1.20939 6
1.87066 7
2.97043 8
-0.01163
0.00718 5
0.00164 2
41
1.18845 6
1.88360 1
2.97339 4
-0.01047
0.00646 7
0.00147 8
42
1.16961
1 1.89524
2.97605 5
-0.00942 0.00582 0.00133
43 1.15265
1.90571 6
2.97844 9
-0.00848
0.00523 8
0.00119 7
44 1.137385 1.915145 2.980605 0.00763- 0.004714 0.001078
45 1.123646 1.92363 2.982544 0.00687- 0.004243 0.00097
46
1.11128 2
1.93126
7 2.98429
-0.00618
0.00381 8
0.00087 3
47
1.10015 3
1.93814 1
2.98586 1
-0.00556
0.00343 7
0.00078 6
48
1.09013 8
1.94432 7
2.98727 5
-0.00501
0.00309 3
0.00070 7
49
1.08112 4
1.94989 4
2.98854 7
-0.00451
0.00278 4
0.00063 6
Dari
table
diatas,
didapat
bahwa
x=1.081124≡1; y=1.949894≡2; z=2.988547≡3
dengan
error x=−0.00451;error y=0.002784;error z=0.000636.DIFERENSIASI NUMERIK
y=x3 −2x2
−x
Metode Selisih Maju
x f(x) f'(x)
nilai
eksak error
0 0 -1
-0.05 -0.05488 -1.0975 -1.1925 -0.095
0.1 -0.119 -1.2825 -1.37 -0.0875
0.15 -0.19163 -1.4525 -1.5325 -0.08
0.2 -0.272 -1.6075 -1.68 -0.0725
0.25 -0.35938 -1.7475 -1.8125 -0.065
0.3 -0.453 -1.8725 -1.93 -0.0575
0.35 -0.55213 -1.9825 -2.0325 -0.05
0.4 -0.656 -2.0775 -2.12 -0.0425
0.45 -0.76388 -2.1575 -2.1925 -0.035
0.5 -0.875 -2.2225 -2.25 -0.0275
0.55 -0.98863 -2.2725 -2.2925 -0.02
0.6 -1.104 -2.3075 -2.32 -0.0125
0.65 -1.22038 -2.3275 -2.3325 -0.005
0.7 -1.337 -2.3325 -2.33 0.0025
0.75 -1.45313 -2.3225 -2.3125 0.01
0.8 -1.568 -2.2975 -2.28 0.0175
0.85 -1.68088 -2.2575 -2.2325 0.025
0.9 -1.791 -2.2025 -2.17 0.0325
0.95 -1.89763 -2.1325 -2.0925 0.04
1 -2 -2.0475 -2 0.0475
Rata-rata error = -0.02375
Metode Selisih Mundur
x f(x) f'(x)
nilai
eksak error
-0.05
0.04487
-0 0 -0.8975 -1 -0.1025
0.05 -0.05488 -1.0975 -1.1925 -0.095
0.1 -0.119 -1.2825 -1.37 -0.0875
0.15 -0.19163 -1.4525 -1.5325 -0.08
0.2 -0.272 -1.6075 -1.68 -0.0725
0.25 -0.35938 -1.7475 -1.8125 -0.065
0.3 -0.453 -1.8725 -1.93 -0.0575
0.35 -0.55213 -1.9825 -2.0325 -0.05
0.4 -0.656 -2.0775 -2.12 -0.0425
0.45 -0.76388 -2.1575 -2.1925 -0.035
0.5 -0.875 -2.2225 -2.25 -0.0275
0.55 -0.98863 -2.2725 -2.2925 -0.02
0.6 -1.104 -2.3075 -2.32 -0.0125
0.65 -1.22038 -2.3275 -2.3325 -0.005
0.7 -1.337 -2.3325 -2.33 0.0025
0.75 -1.45313 -2.3225 -2.3125 0.01
0.8 -1.568 -2.2975 -2.28 0.0175
0.85 -1.68088 -2.2575 -2.2325 0.025
0.9 -1.791 -2.2025 -2.17 0.0325
0.95 -1.89763 -2.1325 -2.0925 0.04
1 -2 -2.0475 -2 0.0475
Rata-rata error = -0.0275
Metode Selisih Tengahan
x f(x) f'(x)
nilai
eksak error
-0.05
0.04487
5 - -0.7925
-0 0 -0.9975 -1 -0.0025
0.05 -0.05488 -1.19 -1.1925 -0.0025
0.1 -0.119 -1.3675 -1.37 -0.0025
0.15 -0.19163 -1.53 -1.5325 -0.0025
0.2 -0.272 -1.6775 -1.68 -0.0025
0.25 -0.35938 -1.81 -1.8125 -0.0025
0.3 -0.453 -1.9275 -1.93 -0.0025
0.35 -0.55213 -2.03 -2.0325 -0.0025
0.4 -0.656 -2.1175 -2.12 -0.0025
0.5 -0.875 -2.2475 -2.25 -0.0025
0.55 -0.98863 -2.29 -2.2925 -0.0025
0.6 -1.104 -2.3175 -2.32 -0.0025
0.65 -1.22038 -2.33 -2.3325 -0.0025
0.7 -1.337 -2.3275 -2.33 -0.0025
0.75 -1.45313 -2.31 -2.3125 -0.0025
0.8 -1.568 -2.2775 -2.28 -0.0025
0.85 -1.68088 -2.23 -2.2325 -0.0025
0.9 -1.791 -2.1675 -2.17 -0.0025
0.95 -1.89763 -2.09 -2.0925 -0.0025
1 -2 - -2
