QUIZ-10-All Problems - y = y x 2 = f x y Euler method y 0 =...

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This means Euler method h= 0.1 i x_i y_i f(x_i, y_i) 0 0 0 0 1 0.1 0 0.01 2 0.2 0 0.04 3 0.3 0 0.09 4 0.4 0.01 0.15 5 0.5 0.03 0.22 6 0.6 0.05 0.31 7 0.7 0.08 0.41 8 0.8 0.12 0.52 9 0.9 0.17 0.64 10 1 0.24 0.76 Final Value y(1) Corrector Predictor Huen's Method i x_i y_i f(x_i, y_i) y_i+1^0 f(x_i+1, y_i+1^0) 0 0 0 0 1 0.1 0 0.01 0 0.01 2 0.2 0 0.04 0 0.04 3 0.3 0.01 0.08 0.01 0.08 4 0.4 0.02 0.14 0.02 0.14 5 0.5 0.04 0.21 0.03 0.22 6 0.6 0.06 0.3 0.06 0.3 7 0.7 0.1 0.39 0.09 0.4 8 0.8 0.14 0.5 0.14 0.5 9 0.9 0.2 0.61 0.19 0.62 10 1 0.27 0.73 0.26 0.74 Final Value y(1) Runge Kutta k1= i x_i y_i f(x_i, y_i) x_i+3/4*h y_i+3/4*k1* k2 0 0 0 0 0.08 0 0.01 1 0.1 0 0.01 0.18 0 0.03 2 0.2 0 0.04 0.28 0.01 0.07 3 0.3 0.01 0.08 0.38 0.01 0.13 4 0.4 0.02 0.14 0.48 0.03 0.2 ) , ( ' 2 y x f x y y = + - = 0 ) 0 ( = y h y x f y y i i i i ) , ( 1 + = + y y y y i i : Corrector : Predictor 1 0 1 + + = = ; 3 2 3 1 1 2 1 1 k h k k y y i i + + = +
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5 0.5 0.04 0.21 0.58 0.05 0.28 6 0.6 0.06
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