11 - Diferensian - Euler1

METODE EULER Metode yang sederhana namun kurang teliti Contoh 1 Selesaikan persamaan: Penyelesaian: y(0,5) = y(0) + f (0;1) 0,5 Kemiringan garis dititik (x0;y0) : dy = f (0;1 8.5 dx sehingga: y (0,5) = 5.25 y = - 0,5X^4 + 4X^3 - 10X2 + 8,5X + 1 nilai eksak pada titik x = 0,5 adalah: y (0,5) = 3.21875 Koreksi k titik awal X = 0 X y eksak dy 0.5 dx y perk % y0 0.00 1.00 8.5 1.00 - 0.25 2.56 4.21875 dari x = 0 sampai x =4 dengan panjang Dx = 0,5 dan Dx = 0,25 DX = yi = yo + f(xo,yo) DX DX =

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Transcript of 11 - Diferensian - Euler1

EulerMETODE EULERMetode yang sederhana namun kurang telitiContoh 1Selesaikan persamaan:dari x = 0 sampai x =4 dengan panjang Dx = 0,5 dan Dx = 0,25Penyelesaian:y(0,5) = y(0) + f (0;1) 0,5Kemiringan garis dititik (x0;y0) :DX = 0.5dy = f (0;1) =8.5dxsehingga:y (0,5) =5.25

y = - 0,5X^4 + 4X^3 - 10X2 + 8,5X + 1nilai eksak pada titik x = 0,5 adalah:y (0,5) =3.21875Koreksi kelsahan:-63.11%titik awal X = 0yi = yo + f(xo,yo) DX

Xy eksakdyDX = 0.5DX = 0.25dxy perk%y perk%y00.001.008.51.00-1.00-0.252.564.218753.1322.04%y10.503.221.255.2563.11%4.1829.85%0.753.28-0.593754.4936.99%y21.003.00-1.55.8895.83%4.3444.79%1.252.59-1.656253.9753.13%y31.502.22-1.255.13130.99%3.5560.21%1.752.00-0.468753.2462.27%y42.002.000.54.50125.00%3.1356.25%2.252.251.468753.2544.57%y52.502.722.254.7574.71%3.6233.05%2.753.342.656254.1825.07%y63.004.002.55.8846.88%4.8421.09%3.254.531.593755.4720.74%y73.504.72-0.257.1350.99%5.8724.34%3.754.31-3.218755.8034.66%y84.003.00-7.57.00133.33%5.0066.67%