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N29 - ME 510 NUMERICAL METHODS FOR ME II EXAMPLE ON...

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ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 EXAMPLE ON RUNGE-KUTTA METHODS y n+1 = y n + h f (t n , y n ) Euler's Method: Heun's Method g11 g12 g62 g64 y , (t f y , t f ) y , (t f 2 h y y n n n 1 n n n n 1 n g14 g14 g14 g32 g14 g14 The Runge-Kutta Order 4 ) K K 2 K 2 (K 6 h y y 4 3 2 1 n 1 n g14 g14 g14 g14 g32 g14 K 1 = f (t n , y n ) ) K 2 h y , 2 h (t f K 1 n n 2 g14 g14 g32 ) K 2 h y , 2 h (t f K 2 n n 3 g14 g14 g32 ) K h y , (t f K 3 n 1 n 4 g14 g32 g14 ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 n 0 1 2 3 4 5 10 100 1000 t / a 0 0.1 0.2
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