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mws_gen_ode_ppt_euler(1) - Euler Method Major All...

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1/10/2010 http://numericalmethods.eng.usf.edu 1 Euler Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Euler Method http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 Euler’s Method Φ Step size, h x y x 0 ,y 0 True value y 1 , Predicted value ( ) ( ) 0 0 , , y y y x f dx dy = = Slope Run Rise = 0 1 0 1 x x y y = ( ) 0 0 , y x f = ( )( ) 0 1 0 0 0 1 , x x y x f y y + = ( ) h y x f y 0 0 0 , + = Figure 1 Graphical interpretation of the first step of Euler’s method
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http://numericalmethods.eng.usf.edu 4 Euler’s Method Φ Step size h True Value y i+1 , Predicted value y i x y x i x i+1 Figure 2. General graphical interpretation of Euler’s method ( ) h y x f y y i i i i , 1 + = + i i x x h = + 1
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