Re: NDSolve can't solve a complex ODE correctly?
- To: mathgroup at smc.vnet.net
- Subject: [mg74906] Re: NDSolve can't solve a complex ODE correctly?
- From: dh <dh at metrohm.ch>
- Date: Tue, 10 Apr 2007 06:04:05 -0400 (EDT)
- References: <evd3uh$5ks$1@smc.vnet.net>
Hi barrow,
you are fooling yourself. Every numerical solution has small numerical
errors. What you see are exatcly these errors of the order of 10^-6. You
can see this by plotting e.g.:
Plot[Evaluate[{a[t]/az[t]}/.sol]-2.07846,{t,1000,2000},
PlotStyle\[Rule]{Hue[1]}];
hope this helps, Daniel
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
>
>