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MathGroup Archive 2000

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Re: When ploting a differential equation, sigularities cause big ugly vertical lines on the graph - how can I get rid of them? By some magic mathematica incantaion?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25178] Re: When ploting a differential equation, sigularities cause big ugly vertical lines on the graph - how can I get rid of them? By some magic mathematica incantaion?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 12 Sep 2000 21:24:22 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <8pklfd$m91@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Ed wrote:
> 
> Howdy All!
> 
> When ploting a differential equation, sigularities cause big ugly
> vertical lines on the graph.
> 
> For example if I am graphing a family of solutions curves, each of
> which decreases exponentially, at least some of them will be treated
> as signularities by mathematica, and the place where they become too
> funky for mathematica, there is an ugly vertical line.
> 
> I would like to plot a function only within a certain range, and when
> it leaves that range I would like mathematica to stop computing the
> function.
> 
> Alternatively I could use any possible advice on how to turn off these
> vertical lines. Here's an example function with these singularities:
> 
> In[2]:=
> Table[NDSolve[{y'[t] == y[t]-y[t]^2/12-4, y[0] == i}, y, {t,
> 0,8}],{i,4,20,4}]
> 
> NDSolve::"ndsz":
>     "At \!\(t\) == \!\(3.62756604743090482`\), step size is
> effectively zero; \
> singularity suspected."
> NDSolve::"ndsz":
>     "At \!\(t\) == \!\(7.25517865610478196`\), step size is
> effectively zero; \
> singularity suspected."
> Out[2]=
> {{{y\[Rule]InterpolatingFunction[{{0.,3.62757}},"<>"]}},{{
>       y\[Rule]InterpolatingFunction[{{0.,7.25518}},"<>"]}},{{
>       y\[Rule]InterpolatingFunction[{{0.,8.}},"<>"]}},{{
>       y\[Rule]InterpolatingFunction[{{0.,8.}},"<>"]}},{{
>       y\[Rule]InterpolatingFunction[{{0.,8.}},"<>"]}}}
> 
> Here's the plotting command I am using:

Hi,

res = Table[
    NDSolve[{y'[t] == y[t] - y[t]^2/12 - 4, y[0] == i}, y, {t, 0, 8}],
{i, 4, 
      20, 4}];

plst = Plot[Evaluate[Sequence @@ #], DisplayFunction -> Identity, 
        AspectRatio -> 1, PlotRange -> {0, 20}, 
        FrameLabel -> {"Fish Population - Fixed Harvesting", 
            y'[t] == y[t] - y[t]^2/12 - 4}, 
        Frame -> 
          True] & /@ ({#, Prepend[Sequence @@ First[Head[#]], First[#]]}
& /@ 
        Flatten[(y[t] /. res)]);

Show[plst, DisplayFunction -> $DisplayFunction]

will do it.
Since plot can only plot multiple functions over a single range, you
have
to use multiple plot commands for every function.
Since your Interpolation[] break somewhere in the interval x in[0,8]
you must find the x-range manual.

Regards
  Jens


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