N30 - ME – 510 NUMERICAL METHODS FOR ME II

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 STABILITY OF RUNGE-KUTTA METHODS 1 (0) y : IC y t d y d g32 g79 g32 y (t) = e g540 t Exact Solution: Numerical Solution: y n+1 = y n P ( g79 h) Euler's Method g11 g12 h 1 y y n 1 n g79 g14 g32 g14 Runge-Kutta Order 2 2 h) ( h 1 y y 2 n 1 n g184 g184 g185 g183 g168 g168 g169 g167 g79 g14 g79 g14 g32 g14 Runge-Kutta Order 4 ! 4 h) ( ! 3 h) ( 2 h) ( h 1 y y 4 3 2 n 1 n g184 g184 g185 g183 g168 g168 g169 g167 g79 g14 g79 g14 g79 g14 g79 g14 g32 g14 ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007-2-1 1 2 3 4 5 6 7 8-3-2-1 1 2 exp(x) 1+x+x*x/2 1+x+x*x/2+x**3/6 1+x+x*x/2+x**3/6+x**4/24 ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 EXAMPLE ON STABILITY OF RUNGE-KUTTA METHODS 1- t 10- y 10 t d y d g32 t - e A (t) y t 10 g32 y (0) = 0 Given: General Solution...
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This note was uploaded on 02/28/2011 for the course ME 510 taught by Professor Dr.faruckarinc during the Spring '11 term at Middle East Technical University.

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N30 - ME – 510 NUMERICAL METHODS FOR ME II

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