Re: NDSolve and Lane-Emden
- To: mathgroup at smc.vnet.net
- Subject: [mg42535] Re: [mg42512] NDSolve and Lane-Emden
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sat, 12 Jul 2003 20:53:15 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Fred,
Try this:
LEeq[n_] := 1/x^2*D[x^2D[y[x], x], x] == -Sign[y[x]]Abs[y[x]]^n
soln = y /. First @ NDSolve[{LEeq[3.3], y'[1] == 0, y[1] == 1}, y,
{x, 1, 10}]
Plot[soln[x], {x, 1, 10}]
The second step could also be done this way:
Clear[soln];
soln[x_] = y[x] /. First @ NDSolve[{LEeq[3.3], y'[1] == 0, y[1] ==
1}, y[x], {x, 1, 10}]
That's mainly a matter of taste.
(I've written the right side of the equation that way to avoid complex
values when y[x] becomes negative, which I'm not sure you want to do.)
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
On Saturday, July 12, 2003, at 05:19 AM, fedgingt at fandm.edu wrote:
> Hi. I have not worked extensively with Mathematica in the past. I am
> working
> with the Lane-Emden equation for a polytropic gas:
> -y[x]^N=1/x^2*D[x^2D[y[x],x],x]. N is the polytropic index. I have
> been using
> NDSolve to find a solution to this equation when N=3.3, 3.35 and 3.4
> for x
> starting a 1. However, I am have trouble with the InterpolatingFunction
> Mathematica gives me. It does not give numerical answers (for
> example, when I
> type y[2]/.% the output Mathematica gives is {y[2]}.) At the same
> time, I am
> able to plot this function. Is there some way to get a result for the
> Lane-Emden that will produce numerical answers? Thanks, Fred
>
>