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Tutorial_4

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

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Tutorial 4 Consider the first order I.V.P. ODE: g1876g1877 g1856g1877 g1856g1876 =sing4666g1876g1877g4667 IC: g1877g46660g4667=1 We want to find g1877g4666g1876g4667 for 0≤g1876≤5 and to estimate g1877g46665g4667 . (a) apply the (explicit) Euler method with Δg1876=0.2 . For an accuracy check, repeat with Δg1876=0.1 . (b) apply a fourth order Runge-Kutta method with Δg1876=0.2 . (c) apply the Euler predictor-corrector method with Δg1876=0.2 . Summary Method g2207g4666g2782g4667 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

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

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