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