Re: 3-D to 2-D slice revisited

• To: mathgroup at smc.vnet.net
• Subject: [mg14246] Re: 3-D to 2-D slice revisited
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 12 Oct 1998 13:51:31 -0400
• Organization: University of Western Australia
• References: <6vf3pc\$dd4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Michael Mihalik wrote:

> I posted a message on here a week or so ago, about taking a slice of a
> 3-D graph, and then taking only one slice of it and looking at it in
> 2-D.  I received some replies, but i don't think that they understood
> the question, so I will copy down exactly what I have entered

soln = NDSolve[{D[y[x,t],t]== D[y[x,t],x,x]*0.01 - D[y[x,t],x],
y[x,0]==If[x>0,0,1], y[0,t]==1,Derivative[1,0][y][1,t]==0} , y,
{x,0,1}, {t,0,2}]

Plot3D[Evaluate[y[x,t]/.First[soln]], {x,0,1}, {t,0,2},
PlotPoints -> 30]

> I want to take the graph generated from the above partial differential
> equation and view the y-z slice at x = 1.

Do you mean the y-t slice at x = 1? If so,

Plot[Evaluate[y[1,t]/.First[soln]], {t,0,2}, PlotPoints -> 30]

>P.S., I've already tried viewing the 3-D plot from just the right
>angle, but it is not good enough to interpolate a line and extract
>certain parameters from it.

Note that the output of NDSolve _is_ an interpolating function -- so
there should be no need to interpolate a line and extraction of
parameters from it should be straightforward.  For example, to find the
slope of the y[1,t] at t = 0.9 (i.e., for the y-t slice at x = 1), you
can use

In[5]:= Derivative[0,1][y][1,0.9]/.First[soln]
Out[5]= 2.6311

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul at physics.uwa.edu.au  AUSTRALIA
http://www.physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

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