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

*To*: mathgroup at smc.vnet.net*Subject*: [mg69355] Re: Why doesn't Mathematica solve this simple differential equation?*From*: Joseph Gwinn <JoeGwinn at comcast.net>*Date*: Thu, 7 Sep 2006 23:59:01 -0400 (EDT)*Organization*: Gwinn Instruments*References*: <eddqq8$3vq$1@smc.vnet.net> djhhr$llh$11smccvnee.neee dm117$cc7$11smccvnee.neee <edom8a$hve$1@smc.vnet.net>

In article <edom8a$hve$1 at smc.vnet.net>, p-valko at tamu.edu wrote: > If you want Mathematica to be smart, let her do the job symbolically: > > In: > DSolve[eqns41, {Vc[t], Il[t]}, t] // First > > Out: > {Il[t] -> Vo/(E^(t/(C1*R1 + C1*R2))*(R1 + R2)), Vc[t] -> Vo/E^(t/(C1*R1 > + C1*R2))} > > In: > % /. {C1 -> 1.0*10^-6, R1 -> 16, R2 -> 27, Vo -> 4.0} > > Out: > {Il[t] -> 0.093023 * E^(-23255.81*t), Vc[t] -> 4. * E^(-23255.81*t)} I did try this. When I do this with the diode equation, the symbolic answer is far from simple, and really isn't very useful. Thanks, Joe > Regards > P.V. > > Joseph Gwinn wrote: > > In article <edjh7r$luh$1 at smc.vnet.net>, > > Joseph Gwinn <JoeGwinn at comcast.net> 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. > > > > > > I just read the Mathematica 5.2 NDSolve Advanced Documentation section > > > on Differential Algebraic Equations. > > > > > > It occurs to me that, aside from the typos, what may be happening is > > > that I'm handing Mathematica something that looks like a Differential > > > Algebraic Equation (DAE) of index exceeding 1, as Mathematica was able > > > to solve the system with one implicit equation (for the diode, with a > > > capacitor but no resistor). > > > > I now have a clean example of the problem: > > > > eqns41 = {Vc'[t] == -Il[t]/C1, Vc[t] == (R1 + R2)*Il[t], Vc[0] == Vo} > > > > eqns42 = eqns41 /. {C1 -> 1.0*10^-6, R1 -> 16, R2 -> 27, Vo -> 4.0} > > > > eqns42soln = NDSolve[eqns42, Vc, {t, 0, 1}] > > > > The above fails: "NDSolve::overdet: There are fewer dependent variables, > > {Vc[t]}, than equations, so the system is underdetermined." > > > > eqns41a = Eliminate[eqns41, Il[t]] > > > > eqns42a = eqns41a /. {C1 -> 1.0*10^-6, R1 -> 16, R2 -> 27, Vo -> 4.0} > > > > eqns42asoln = NDSolve[eqns42a, Vc, {t, 0, 1}] > > > > The above works. > > > > Eliminate[] cannot make a self-consistent system from an inconsistent > > system, so the original system must also be consistent. Yet it fails. > > > > Does Mathematica think that this system is some kind of complicated DAE? > > Apparently, given that Eliminate[] solves the problem. Why couldn't > > NDSolve do its own algabraic reduction? The variable Il[t] was not > > requested as an output. > > > > I have a few more such examples, so the issue isn't restricted to this > > example. > > > > The other issue is that *all* combinations of real electronic components > > (that is, circuits) lead to a numerically solvable system of ODEs, > > because all circuits will do something real if constructed and tested. > > So, aside from eliminating silly mistakes, this should not be hard, and > > I'm trying to figure out the root cause of these random-appearing > > failures. Mathematica is probably trying to do something that ordinary > > circuit simulators (such as SPICE) wouldn't dream of. > > > > Joe Gwinn

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