mws_com_ode_txt_runge4th_Examples

mws_com_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 Computer Engineering Example 1 A rectifier-based power supply requires a capacitor to temporarily store power when the rectified waveform from the AC source drops below the target voltage. To properly size this capacitor a first-order ordinary differential equation must be solved. For a particular power supply, with a capacitor of μ F 150 , the ordinary differential equation to be solved is       0 , 04 . 0 2 120 cos 18 max 1 . 0 10 150 1 ) ( 6 t v t dt t dv 0 ) 0 ( v Using the Runge-Kutta 4 th order method, find voltage across the capacitor at s 00004 . 0 t . Use step size s 0.00002 h . Solution     0 , 04 . 0 2 120 cos 18 max 1 . 0 10 150 1 6 v t dt dv      0 , 04 . 0 2 120 cos 18 max 1 . 0 10 150 1 , 6 v t v t f  h k k k k v v i i 4 3 2 1 1 2 2 6 1 For 0 i , 0 0 t , 0 0 v  0 0 1 , v t f k  0 , 0 f       0 , 04 . 0 0 2 0 120 cos 18 max 1 . 0 10 150 1 6   0 , 400 max 1
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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_com_ode_txt_runge4th_Examples - Chapter 08.04...

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