1) Numerical precision, 2) Bug in Plot?

• To: mathgroup at smc.vnet.net
• Subject: [mg29856] 1) Numerical precision, 2) Bug in Plot?
• From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
• Date: Sat, 14 Jul 2001 01:36:46 -0400 (EDT)
• Organization: Universitaet Regensburg
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,
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

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.

Any suggestions?
Thank you and best regards,
Johannes Ludsteck

<><><><><><><><><><><><><><><><><><>
Johannes Ludsteck
Institut fuer Volkswirtschaftslehre
Lehrstuhl Prof. Dr. Moeller
Universitaet Regensburg
Universitaetsstrasse 31
93053 Regensburg
Tel +49/0941/943-2741

```

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