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

• To: mathgroup at smc.vnet.net
• Subject: [mg69268] Re: Why doesn't Mathematica solve this simple differential equation?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 4 Sep 2006 04:47:09 -0400 (EDT)
• Organization: The University of Western Australia
• References: <eddqq8\$3vq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <eddqq8\$3vq\$1 at smc.vnet.net>,
Joseph Gwinn <JoeGwinn at comcast.net> wrote:

> 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.

There is an NDSolve example involving a diode in the built-in
documentation. Evaluate

FrontEndExecute[FrontEnd`HelpBrowserLookup[

and click on the "Demos" link.

> 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}]
>
> 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}

You mean

eqns22 = eqns21 /. {C1 -> 1.0*10^-6, R1 -> 16, Is -> 10^-13} ?

Even so, your equations are inconsistent.

> eqns22soln = NDSolve[eqns22, Vc, {t, 0, 1}]
>
> Both approaches fail with Mathematica complaining that "NDSolve::ndode:
> Input is not an ordinary differential equation".

Which is not suprising.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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