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MathGroup Archive 2006

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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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