Runge-Kutta 4th Order Method

# Runge-Kutta 4th Order Method - Runge4thOrderMethod...

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05/01/11 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

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Runge-Kutta 4 th  Order Method      http://numericalmethods.eng.usf.edu
http://numericalmethods.eng.usf.edu 3 Runge-Kutta 4 th  Order Method where ( 29 h k k k k y y i i 4 3 2 1 1 2 2 6 1 + + + + = + ( 29 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 ( 29 h k y h x f k i i 3 4 , + + = For 0 ) 0 ( ), , ( y y y x f dx dy = = Runge Kutta 4 th  order method is given by

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http://numericalmethods.eng.usf.edu 4 How to write Ordinary Differential  Equation Example ( 29 5 0 , 3 . 1 2 = = + - y e y dx dy x is rewritten as ( 29 5 0 , 2 3 . 1 = - = - y y e dx dy x In this case ( 29 y e y x f x 2 3 . 1 , - = - How does one write a first order differential equation in the form of ( 29 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 ( 29 ( 29 K dt d 1200 0 , 10 81

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## This note was uploaded on 05/01/2011 for the course CHBE 2120 taught by Professor Gallivan during the Spring '07 term at Georgia Institute of Technology.

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Runge-Kutta 4th Order Method - Runge4thOrderMethod...

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