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Re: directionfields from StreamPlot looks different from

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100468] Re: [mg100444] directionfields from StreamPlot looks different from
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 5 Jun 2009 03:00:36 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200906040732.DAA11830@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

You're not.  For the "direction field" of a 1-dimensional ordinary 
differential equation y' == f[t, y], the vector field you want to plot 
is {1, f[t,y]}.  So...

   streams =
   StreamPlot[{1, t^2 - y}, {t, -4, 4}, {y, -2, 10},
      StreamStyle -> Directive[Orange]];
   sol = Table[NDSolve[{y'[t] == t^2 - y[t], y[0] == y0}, y[t],
            {t, -4, 4}], {y0, 0, 6, 0.5}];
   solutionCurves =
      Plot[y[t] /. sol, {t, -4, 4}, PlotRange -> {{-4, 4}, {-2, 10}}];
   Show[{solutionCurves, streams}

Note that you do not need any parentheses around t^2. And in the current 
version of Mathematica, you no longer need to wrap y[t]/.sol with 
Evaluate -- unless you would like the curves automatically to be given 
different colors.

sean_incali at yahoo.com wrote:
> I don't think I'm using StreamPlot properly.
> 
> Consider the following non-autonomous ODE
> 
> y'[t] == (t^2) - y[t]
> 
> Solutions for various ICs can be viewed by the following.
> 
> sol= Table[NDSolve[{y'[t] == (t^2) - y[t], y[0] == y0}, y[t], {t, -4,
> 4}], {y0, 0, 6, 0.5}];
> 
> Plot[Evaluate[y[t] /. sol], {t, -4, 4}, PlotRange -> {{-4, 4}, {-2,
> 10}}]
> 
> Shouldn't Vector fields be similar to the solutions above? If I plot t
> on x-axis vs. t^2-y on y axis...
> 
> VectorPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}]
> 
> StreamPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}]
> 
> I don't get similar results...
> 
> What is the reason for this?
> 
> Thanks much in advance
> 
> Sean
> 
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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