       Re: Why doesn't Mathematica solve this simple differential equation?

• To: mathgroup at smc.vnet.net
• Subject: [mg69294] Re: Why doesn't Mathematica solve this simple differential equation?
• From: Joseph Gwinn <JoeGwinn at comcast.net>
• Date: Tue, 5 Sep 2006 05:31:14 -0400 (EDT)
• Organization: Gwinn Instruments
• References: <eddqq8\$3vq\$1@smc.vnet.net> <edg8jf\$ghs\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <edg8jf\$ghs\$1 at smc.vnet.net>, Peter Pein <petsie at dordos.net>
wrote:

> Joseph Gwinn schrieb:
> > Here is the system I'm trying to solve.  It's an electrical circuit
> > consisting of a capacitor C1 (with initial voltage 4.0 volts), a
> > resistor R1, and a diode in series.
> >
> >
> > Approach 1:
> >
> > eqns11 = {Q1'[t] == -Iloop[t], Q1[t] == C1*Vc[t],     Vr[t] ==
> > R1*Is*Exp[Vd[t]/0.026], Vc[t] == Vr[t] + Vd[t], Vc == 4.0}
> >
> > eqns12 = eqns11 /. {C1 -> 1.0*10^-6, R1 -> 16, Is -> 10^-13}
> >
> > eqns12soln = NDSolve[eqns12, Q1, {t, 0, 1}]
> >
>
> You want to solve for Q1. Unless there is an dependency in a previous
> definition of Iloop between Q1 and the voltages, the relevant equations
> remaining are:
> Q1'[t] == -Iloop[t] and Q1[t] == C1*Vc[t]
> with unknown(?) Iloop. Obviously this can not be solved.

So, it's underdetermined.

> > Approach 2:
> >
> > eqns21 = {Vc'[t] == -Id[t]/C1, Vc[t] == 0.026*Log[Id[t]/Is] + R1*Id[t],
> > Vc == 4.0}
> >
> > eqns22 = eqns11 /. {C1 -> 1.0*10^-6, R1 -> 16, Is -> 10^-13}
> >
> > eqns22soln = NDSolve[eqns22, Vc, {t, 0, 1}]
>
> The same happens here more functions (all undefined?) than equations.

When I fixed the above system (to say eqns22=eqns21...), that's the
complaint I now get.

Anyway, I'll focus on that.

Thanks,

Joe

> > Both approaches fail with Mathematica complaining that "NDSolve::ndode:
> > Input is not an ordinary differential equation".
> >
> > Another, simpler, problem (same circuit but without the R1) solves
> > happily, so long as I eliminate all intermediate variables manually.
> >
> > eqns1 = {Vd'[t] == -Is*Exp[Vd[t]/0.026]/C, Vd == 4.0}
> >
> > eqns2 = eqns1 /. {C -> 1.0*10^-6, Is -> 10^-13}
> >
> > eqns2soln = NDSolve[eqns2, Vd, {t, 0, 1}]
> >
>
> One function, one equation - Mathematica is happy
>
> >
> > Any ideas?
> >
> > Joe Gwinn
> >
>
> consider this example, where elimination is trivial:
>
> In:=
> DSolve[{f'[x] == g[x] - f[x], g[x] == Sin[x]}, f[x], x]
>  From In:=
> "DSolve::deqx: Supplied equations are not differential equations of the
> given functions."
> Out=
> DSolve[{f'[x] == g[x] - f[x], g[x] == Sin[x]}, f[x], x]
>
> and
>
> In:=
> DSolve[
>    Eliminate[{f'[x] == g[x] - f[x], g[x] == Sin[x]}, g[x]],
>   f, x]
>
> solves the deq.
>
> HTH
> Peter

```

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