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Re: 1) Numerical precision, 2) Bug in Plot?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg29872] Re: [mg29856] 1) Numerical precision, 2) Bug in Plot?
*From*: BobHanlon at aol.com
*Date*: Sun, 15 Jul 2001 00:58:59 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 2001/7/14 2:11:21 AM,
johannes.ludsteck at wiwi.uni-regensburg.de writes:
>if I am right, it is simple to confuse
>Mathematica.
>I obtained a numerical solution for the following
>simple differential equation:
>
>kd=k/.NDSolve[
> {k'[t]==Sqrt[0.2 Exp[0.01 t] k[t]]-0.2 k[t],
> k[0]==1},k,{t,0,500},][[1]]
>
>Since I guessed that the growth rate of the
>solution ks converges to a constant, I computed
>an approximation to the growth rate of kd by
>differentiating Log[kd] with respect to time:
>
>grkd[t_]:=Block[{z},D[Log[kd[z]],z]/.z->t]
>
>and plotted it for values of t near to the
>supposed steady state:
>
>Plot[grkd[t],{t,300,500}]
>
>I was surprised when I looked at the plot because
>of two problems.
>The first one is that the graph is oscillatory
>and I cannot figure out whether this is a problem
>of numerical precision or a characteristic of the
>solution.
>The second one which probably is caused by a BUG
>in Mathematica is that the y-axis grids have
>identical numbers: 0.01, 0.01 0.01 which of
>course, cannot be true, since the points are not
>identical.
>
Since you are plotting a constant, Mathematica zoomed in until it was able to
see variation (numerical quantum noise). The plot is zoomed in to so small of
a range that all of the labels are identical to the precision of the
labelling. Manually set the PlotRange to see the desired Plot.
Plot[grkd[t], {t, 300, 500}, PlotRange -> {0.001, 0.012}, Frame -> True,
Axes -> False];
Bob Hanlon
Chantilly, VA USA
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