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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: [mg69243] Re: Why doesn't Mathematica solve this simple differential equation?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 3 Sep 2006 23:46:27 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <eddqq8$3vq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Joseph Gwinn 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.  
> 
> 
> 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}]

Let's try this one:

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}

--> {Derivative[1][Q1][t] == -Iloop[t], Q1[t] == C1*Vc[t], Vr[t] == 
E^(38.46153846153846*Vd[t])*Is*R1, Vc[t] == Vd[t] + Vr[t], Vc[0] == 4.}

eqns12= eqns11/. { C1-> 1.0* 10^ -6, R1->16, Is-> 10^ -13}

--> {Derivative[1][Q1][t] == -Iloop[t], Q1[t] == 1.*^-6*Vc[t], Vr[t] == 
E^(38.46153846153846*Vd[t])/625000000000, Vc[t] == Vd[t] + Vr[t], Vc[0] 
== 4.}

If I follow you correctly, you want to solve for the function Q1[t], 
function that you have already defined as 1.*^-6*Vc[t], that is Q1[t] 
depends on the function Vc[t], which is itself defined as the sum of 
functions that depends on another function Vd[t] that is defined 
nowhere. Moreover, the derivative of Q1[t] is also specified as being 
equal to another undefined function Iloop[t]...

You wonder then why NDSolve complains about the input not being an ODE?

eqns12soln= NDSolve[ eqns12,Q1, { t,0,1}]

--> NDSolve::"ndode" : "Input is not an ordinary differential equation. 
More...

Jean-Marc


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