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Re: 1) Numerical precision, 2) Bug in Plot?


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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