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MathGroup Archive 2007

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Re: a problem about NDSolve and NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80200] Re: a problem about NDSolve and NIntegrate
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 14 Aug 2007 07:16:53 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f9emog$lpq$1@smc.vnet.net> <f9p6g1$s1r$1@smc.vnet.net>

lynn wrote:
<snip>

> Thanks for your pointing out my faults.
> 
> I miss-typed it when I tried to simplize my equation.
> 
> But my original problem still exist,
> 
> The following is the original equation,
> 
> f[ _?NumberQ] := y[ ] /. NDSolve[{
>   2 y'[ ] y[ ] +
>       y''[ ] y[ ] -
>           (y'[ ])^2 ==   y[ ], y[0.00001] == 1, y'[0.00001] == =
> 0}, y,
> { ,
>                0.00001,  }, MaxSteps -> 1000][[1]]
> 
> then f[5]=InterpolatingFunction[{{0.00001, 5.}}, <>][ ]
> 
> and I want to integrate it y[ ] with a  ,
> 
> \!\(g[w_?NumberQ,  _?NumberQ] := 2\
>       NIntegrate[\  \/y[ ]=D7 \/\@\( \^2 - w\^2\), { , w,  },
> MaxRecursion -> \
> 10]\)
> 
> But I can't get correct answer when ask for such as g[1,2]...

Your post does not make any sense: do not use any special character set 
when posting to Usenet. (Or use the Ingolf Dahl's "SetFaceAndFont" 
palette. See http://library.wolfram.com/infocenter/MathSource/5752/)

I believe that f is defined more or less as follows

In[1]:= f[c_?NumberQ] :=
  y[x] /. NDSolve[{2 y'[x] y[x] + y''[x] y[x] - (y'[x])^2 == y[x],
      y[0.00001] == 1, y'[0.00001] == 0}, y, {x , 0.00001, c},
     MaxSteps -> 1000][[1]]

So you can get an interpolating function with

In[2]:= f[5]

Out[2]= InterpolatingFunction[][x]

and also plot it as in

In[3]:= Plot[Evaluate@f[5], {x, 0.00001, 5}]

[... graphic deleted ...]

As far as I can see in the posted mess, g does not use f, and y[x] is 
still *NOT* defined outside of f (this have already been pointed out by 
Jens-Peer Kuska a couple of days ago); therefore g has no knowledge of 
what could possibly be y[x].

-- 
Jean-Marc


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