tp geokom ranty 15 mei 2015
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TUGAS PENDAHULUAN GEOKOMPUTASI
Bayu Rezky 1207045059
FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAMFISIKA KONSENTRASI GEOFISIKAUNIVERSITAS MULAWARMANSAMARINDA2015
Soal !Terdapat persamaan berikut :Jika diketahui y = 0.2 dari y = 0 sampai y = 10 dengan x(0) = 1a. Berapakah nilai f(y,x) jika menggunakan metode euler?b. Berapakah masing-masing erornya untuk tiap yc. Bagaimana benuk grafiknya? jelaskan!
Penyelesaian
Eksaknya
Penyelesaian numerikPersamanaan : x1 = x0 + f(y0,x0)xDari kondisi awal pada y = 0 nilai fungsi x(0) = 1, sehingga :xn = x(0) + f (x) xx1 = 1 + 20 (0.2)x1= 5nilai eksak pada titik x = 0.2x (0.2) = = 4.99Nilai error : = x 100%= x 100 %= -0.18498 %
Jawaban :Diketahui :Fx(0)
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Hasil :Xx eksaky = 0.2
x perk (%)
01.0010
0.24.995-0.18498
0.48.939-0.79272
0.612.4213-4.68351
0.814.6117-16.3425
114.2321-47.5755
1.29.5725-161.136
1.4-1.46292087.412
1.6-21.3633254.5087
1.8-52.9937169.8309
2-99.5641141.1812
2.2-164.6445127.3318
2.4-252.1249119.4349
2.6-366.2053114.473
2.8-511.3657111.1467
3-692.3961108.8101
3.2-914.3265107.1091
3.4-1182.4469105.8354
3.6-1502.2873104.8593
3.8-1879.5877104.0967
4-2320.2881103.491
4.2-2830.5285103.003
4.4-3416.6089102.6049
4.6-4084.9993102.2766
4.8-4842.3097102.0032
5-5695.25101101.7734
5.2-6650.70105101.5788
5.4-7715.57109101.4127
5.6-8896.90113101.2701
5.8-10201.77117101.1469
6-11637.32121101.0398
6.2-13210.71125100.9462
6.4-14929.14129100.8641
6.6-16799.80133100.7917
6.8-18829.87137100.7276
7-21026.51141100.6706
7.2-23396.83145100.6197
7.4-25947.89149100.5742
7.6-28686.66153100.5333
7.8-31620.05157100.4965
8-34754.84161100.4632
8.2-38097.71149100.3911
8.4-41655.19169100.4057
8.6-45433.66173100.3808
8.8-49439.37177100.358
9-53678.33181100.3372
9.2-58156.40185100.3181
9.4-62879.22189100.3006
9.6-67852.19193100.2844
9.8-73080.48197100.2696
10-78569.00201100.2558
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