Re: Why doesn't Mathematica solve this simple differential equation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg69289] Re: Why doesn't Mathematica solve this simple differential equation?*From*: Joseph Gwinn <JoeGwinn at comcast.net>*Date*: Tue, 5 Sep 2006 05:31:08 -0400 (EDT)*Organization*: Gwinn Instruments*References*: <eddqq8$3vq$1@smc.vnet.net> <edg7uj$gds$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <edg7uj$gds$1 at smc.vnet.net>, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote: > 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. No, Vd is defined implicitly, in the equation "Vr[t]== R1*Is* Exp[Vd[t]/0.026]". The simplified diode equation is Id=Is*Exp[Vd/0.026]. This form can be inverted, but not so easily done with the full-strength Schottky equation, and it's best to keep the diode equation in standard form. I wondered in Mathematica would be happy with one of the equations in the system being implicit. That's why I tried approach 2. > 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... It turns out that this error was due to an error in the substitutions just before. When the substitution is fixed, the error message changes to a complaint about the system being underdetermined. So that's where I'll dig. Apparently, I need to include more of the physics. Thanks, Joe