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

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ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 EXAMPLE ON RUNGE-KUTTA METHODS y n+1 = y n + h f (t n , y n ) Euler's Method: Heun's Method g G ± ² y , (t f y , t f ) y , (t f 2 h y y n n n 1 n n n n 1 n ³ ³ ³ ´ ³ ³ The Runge-Kutta Order 4 ) K K 2 K 2 (K 6 h y y 4 3 2 1 n 1 n ³ ³ ³ ³ ´ ³ K 1 = f (t n , y n ) ) K 2 h y , 2 h (t f K 1 n n 2 ³ ³ ´ ) K 2 h y , 2 h (t f K 2 n n 3 ³ ³ ´ ) K h y , (t f K 3 n 1 n 4 ³ ´ ³ ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 n 0 1 2 3 4 5 10 100 1000 t / a 0 0.1 0.2 0.3 0.4 0.5 1.0 10.0 100.0 y exact 1 0.90484
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