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N25 - ME 510 NUMERICAL METHODS FOR ME II EULERS METHOD y n...

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ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 EULER’S METHOD: n+1 n n n y = y + h f(t ,y ) 2 local h E = y''( ) 2! g91 2 total n n n n 0 1 h E = y''( ) 2! h h = y''( ) h y''( ) (t - t ) 2! 2! h g91 g91 g91 g32 g118 g166 g166 g166 Local Error: Total or Overall Error: Euler’s method is an order 1 method, i.e., the overall error is proportional to the first power of the step size, h ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 Geometrical Interpretation of Euler’s method
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ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111
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