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MathGroup Archive 2007

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NDSolve can't solve a complex ODE correctly?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74870] NDSolve can't solve a complex ODE correctly?
  • From: "Barrow" <GRseminar at gmail.com>
  • Date: Mon, 9 Apr 2007 06:13:51 -0400 (EDT)

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



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