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MathGroup Archive 2007

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Re: NDSolve can't solve a complex ODE correctly?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74908] Re: NDSolve can't solve a complex ODE correctly?
  • From: "Barrow" <GRseminar at gmail.com>
  • Date: Wed, 11 Apr 2007 01:52:40 -0400 (EDT)
  • References: <evd3uh$5ks$1@smc.vnet.net><evfknm$75t$1@smc.vnet.net>

On 4=A4=EB10=A4=E9, =A4U=A4=C85=AE=C917=A4=C0, "Kevin J. McCann" <k...@Kevi=
nMcCann.com> wrote:
> You should try plotting the individual functions. They are growing
> exponentially. I suspect that this explains why they don't converge
> (numerically) to each other. They are on the order of 10^300 at larger
> values of t.
>
>
Oh sorry, I found just now that, the analytical result is a'[t]/a[t]
converges to az'[t]/az[t], NOT a[t] converges to az[t]. And, the
result obtained by NDSolve of Mathematica respects that.
Thanks anyway!

>
> Barrow wrote:
> > Dear all,
> >    I have two coupled ordinary differential equations which satisfied
> > by two functions, a(t) and az(t). It can be shown analitically that as
> > t approaches infinity, a(t) approaches az(t). But the numerical
> > solution given by Mathematica doesn't agree this.
> >   Here is my code:
> > -----------------------
> > lam = 1;
> > eqb = ((a'[t]/a[t])^2 + 2a'[t]*az'[t]/a[t]/az[t] == lam);
> > eqaz = (3(a'[t]/a[t])^2 + 2(a''[t]/a[t] - (a'[t]/a[t])^2) == lam);
> > sol = NDSolve[{eqb, eqaz, a[0] == 1, az[0] == .5, a'[0] ==
= .6}, {a[t],
> > az[t]}, {t, 0, 2000}, MaxSteps -> 20000];
> > Plot[Evaluate[{a[t]/az[t]} /. sol], {t, 0, 2000}, PlotStyle ->
> > {Hue[1]}];
> > ----------------------------------
> > The result of the plot is an oscillation around 2.07846 which is
> > really strange.
> > Is there anything I didn't noticed about NDSolve or any method to
> > improve my coding?
> > Thanks very much!
> > Cheers.        Barrow- =C1=F4=C2=C3=B3Q=A4=DE=A5=CE=A4=E5=A6r -
>
> - =C5=E3=A5=DC=B3Q=A4=DE=A5=CE=A4=E5=A6r -




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