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