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mws_civ_ode_txt_euler_Examples

mws_civ_ode_txt_euler_Examples - Chapter 08.02 Eulers...

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08.02.1 Chapter 08.02 Euler’s 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 Euler’s 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 , The Euler’s method reduces to h C t f C C i i i i , 1 For 0 i , 0 0 t , 7 0 10 C h C t f C C 0 0 0 1 , 5 . 3 10 , 0 10 7 7 f 5 . 3 ) 10 ( 06 . 0 10 7 7 5 . 3 10 6 10 5 7 3 6 parts/m 10 9 . 7 1 C is the approximate concentration of bacteria at h t t t 0 1 5 . 3 0 weeks 5 . 3 3 6 1

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mws_civ_ode_txt_euler_Examples - Chapter 08.02 Eulers...

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