mws_civ_ode_txt_runge2nd_Examples

# mws_civ_ode_txt_runge2nd_Examples - Chapter 08.03...

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08.03.1 Chapter 08.03 Runge-Kutta 2nd Order Method for Ordinary Differential Equations-More Examples Civil Engineering Example 1 A polluted lake has an initial concentration of a bacteria of 3 7 parts/m 10 , while the acceptable level is only 3 6 parts/m 10 5 . The concentration of the bacteria will reduce as fresh water enters the lake. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by 7 10 ) 0 ( , 0 06 . 0 C C dt dC Using Runge-Kutta 2 nd order method and a step size of 3.5 weeks, find the concentration of the pollutant after 7 weeks. Solution C dt dC 06 . 0  C C t f 06 . 0 , Per Heun’s method h k k C C i i 2 1 1 2 1 2 1  i i C t f k , 1  h k C h t f k i i 1 2 , For 7 0 0 10 , 0 , 0 C t i  0 0 1 , C t f k   7 10 , 0 f ) 10 ( 06 . 0 7

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## This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_civ_ode_txt_runge2nd_Examples - Chapter 08.03...

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