I'm learning circuit modeling recently, and got stuck by a simply serial circuit sample(shown in the attachment), here're equations I wrote for the sample, but I have no idea what initial conditions and algorithm I can use to solve it, could any one give me a hand or some tips?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]i_{21}+{\int_0}^t \frac{V_3-V_1}{L} d\tau =0[/tex]

[tex]i_{12}+\frac{GND-V_2}{R} =0[/tex]

[tex]{\int_0}^t \frac{V_1-V_3}{L} d\tau + C \cdot (\frac{dGND}{dt}-\frac{dV_3}{dt}) =0[/tex]

[tex]C \cdot (\frac{dV_3}{dt}) + \frac{V_2-GND}{R}=0[/tex]

where GND=0 V is constant, I see that [itex]i_{12}=-i_{21}[/itex] can be used to reduce the equations, but then the remaining equations are 2nd order diff equations, how do computers solve this?

[tex]{\int_0}^t \frac{V_2-V_1}{L} d \tau = \frac{-V_2}{R}[/tex]

[tex]{\int_0}^t \frac{V_1-V_3}{L} d\tau + C \cdot -\frac{dV_3}{dt} =0[/tex]

[tex]C \cdot (\frac{dV_3}{dt}) + \frac{V_2}{R}=0[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need some help on Circuit modeling(1 sample)

**Physics Forums | Science Articles, Homework Help, Discussion**