mws_civ_ode_txt_runge4th_Examples

mws_civ_ode_txt_runge4th_Examples - Chapter 08.04...

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Chapter 08.04 Runge-Kutta 4th 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 the Runge-Kutta 4 th order method, find the concentration of the pollutant after 7 weeks. Take a step size of 3.5 weeks. Solution C dt dC 06 . 0  C C t f 06 . 0 ,  h k k k k C C i i 4 3 2 1 1 2 2 6 1 For 0 i , 0 0 t , 7 0 10 C  0 0 1 , C t f k   7 10 , 0 f   7 10 06 . 0 600000 h k C h t f k 1 0 0 2 2 1 , 2 1  5 . 3 600000 2 1 10 , 5 . 3 2 1 0 7 f  8950000 , 75 . 1 f ) 8950000 ( 06
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mws_civ_ode_txt_runge4th_Examples - Chapter 08.04...

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