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]

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# Need some help on Circuit modeling(1 sample)

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