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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: [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[0] == 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[0] == 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[0] == 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[4]:=
> DSolve[{f'[x] == g[x] - f[x], g[x] == Sin[x]}, f[x], x]
>  From In[4]:=
> "DSolve::deqx: Supplied equations are not differential equations of the 
> given functions."
> Out[4]=
> DSolve[{f'[x] == g[x] - f[x], g[x] == Sin[x]}, f[x], x]
> 
> and
> 
> In[5]:=
> 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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