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MathGroup Archive 2001

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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 
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.

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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