Tutorial_4

Tutorial_4 - Tutorial 4 Consider the first order I.V.P....

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Unformatted text preview: Tutorial 4 Consider the first order I.V.P. ODE: gG ¡G ¡g = sin¢gG£ IC: G¢0£ = 1 We want to find G¢g£ for 0 ≤ g ≤ 5 and to estimate G¢5£ . (a) apply the (explicit) Euler method with Δg = 0.2 . For an accuracy check, repeat with Δg = 0.1 . (b) apply a fourth order Runge-Kutta method with Δg = 0.2 . (c) apply the Euler predictor-corrector method with Δg = 0.2 . Summary Method ¤¢¥£ Explicit Euler ∆x = 0.2 1.9033 Explicit Euler ∆x = 0.1 1.8506 4 th order Runge-Kutta ∆x = 0.2 1.7964 Euler Predictor-Corrector ∆x = 0.2 1.6816 (a) Explicit Euler A4 = 0 B4 = 1 C4 = 1 D4 = A4+$B$1 E4 = B4+$B$1*C4 A5 = D4 B5 = E4 C5 = SIN(A5*B5)/(A5*B5) Copy cells down A B C D E 1 dx = 0.2 2 3 x i y i F i x i+1 y i+1 4 0.0 1.0000 1.0000 0.2 1.2000 5 0.2 1.2000 0.9904 0.4 1.3981 6 0.4 1.3981 0.9487 0.6 1.5878 7 0.6 1.5878 0.8554 0.8 1.7589 8 0.8 1.7589 0.7012 1.0 1.8991 9 1.0 1.8991 0.4984 1.2 1.9988 10 1.2 1.9988 0.2820 1.4 2.0552 11 1.4 2.0552 0.0908 1.6 2.0734 12 1.6 2.0734 -0.0527 1.8 2.0628 13 1.8 2.0628 -0.1457 2.0 2.0337 14 2.0 2.0337 -0.1965 2.2 1.9944 15 2.2 1.9944 -0.2160 2.4 1.9512 16 2.4 1.9512 -0.2134 2.6 1.9085 17 2.6 1.9085 -0.1953 2.8 1.8695 18 2.8 1.8695 -0.1656 3.0 1.8364 19 3.0 1.8364 -0.1269 3.2 1.8110 20 3.2 1.8110 -0.0809 3.4 1.7948 21 3.4 1.7948 -0.0295 3.6 1.7889 22 3.6 1.7889 0.0243 3.8 1.7937 23 3.8 1.7937 0.0746 4.0 1.8087 24 4.0 1.8087 0.1126 4.2 1.8312 25 4.2 1.8312 0.1283 4.4 1.8568 26 4.4 1.8568 0.1163 4.6 1.8801 27 4.6 1.8801 0.0810 4.8 1.8963 28 4.8 1.8963 0.0348 5.0 1.9033 29 5.0 1.9033 dx = 0.1 x i y i F i x i+1 y i+1 0.0 1.0000 1.0000 0.1 1.1000 0.1 1.1000 0.9980 0.2 1.1998 0.2 1.1998 0.9904 0.3 1.2988 0.3 1.2988 0.9749 0.4 1.3963 0.4 1.3963 1....
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This note was uploaded on 09/16/2011 for the course ME 303 taught by Professor Serhiyyarusevych during the Spring '10 term at Waterloo.

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Tutorial_4 - Tutorial 4 Consider the first order I.V.P....

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