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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: [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[
    "DemosLink", "Chaotic Circuit"]]

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[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} ?

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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