mws_gen_ode_ppt_runge4th(1)

# mws_gen_ode_ppt_runge4th(1) -...

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Unformatted text preview: 1/10/2010 http://numericalmethods.eng.usf.edu 1 Runge 4 th Order Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates Runge-Kutta 4 th Order Method http://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu 3 Runge-Kutta 4 th Order Method where ( ) h k k k k y y i i 4 3 2 1 1 2 2 6 1 + + + + = + ( ) i i y x f k , 1 = + + = h k y h x f k i i 1 2 2 1 , 2 1 + + = h k y h x f k i i 2 3 2 1 , 2 1 ( ) h k y h x f k i i 3 4 , + + = For ) ( ), , ( y y y x f dx dy = = Runge Kutta 4 th order method is given by http://numericalmethods.eng.usf.edu 4 How to write Ordinary Differential Equation Example ( ) 5 , 3 . 1 2 = = + − y e y dx dy x is rewritten as ( ) 5 , 2 3 . 1 = − = − y y e dx dy x In this case ( ) y e y x f x 2 3 . 1 , − = − How does one write a first order differential equation in the form of ( ) y x f dx dy , = http://numericalmethods.eng.usf.edu 5 Example A ball at 1200K is allowed to cool down in air at an ambient temperature of 300K. Assuming heat is lost only due to radiation, the differential equation for the temperature of the ball is given by ( ) ( ) K dt d 1200 , 10 81 10 2067 . 2 8 4 12 = θ × −...
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mws_gen_ode_ppt_runge4th(1) -...

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