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Re: Why doesn't Mathematica solve this simple differential equation?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg69293] Re: Why doesn't Mathematica solve this simple differential equation?
*From*: Joseph Gwinn <JoeGwinn at comcast.net>
*Date*: Tue, 5 Sep 2006 05:31:13 -0400 (EDT)
*Organization*: Gwinn Instruments
*References*: <eddqq8$3vq$1@smc.vnet.net> <edgpfu$oie$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <edgpfu$oie$1 at smc.vnet.net>,
Paul Abbott <paul at physics.uwa.edu.au> wrote:
> 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[
> "DemosLink", "Chaotic Circuit"]]
>
> and click on the "Demos" link.
It's a good example, even if their diode model is nonphysical.
> > 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[0] == 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[0] == 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} ?
Yes. The error message changes to a complaint that the system is
underdetermined. Actually, this is progress, because the nature of
whatever I'm missing is now better constrained.
> Even so, your equations are inconsistent.
I'm guessing that it isn't enough for me to give the differential
(Vc'[t]==Q'[t]/C1), I also need to give the other piece of information
from the physics (Vc[t]==Q[t]/C).
Thanks,
Joe
> > 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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