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Re: Reasonable integration speed? (24 hrs and counting)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68035] Re: Reasonable integration speed? (24 hrs and counting)
  • From: "ben" <benjamin.friedrich at gmail.com>
  • Date: Fri, 21 Jul 2006 05:37:23 -0400 (EDT)
  • References: <e9nkvm$9vo$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi

My version of Mathematica cant solve this integral (it gets returned
unevaluated),
to I guess your kernel simply hang up (happens occasionaly).

In[19]:=
Integrate[
  Cos[(2*n+1)*Pi*
        x/d]*(Exp[-I*k*f[x]]/(4*Pi*
                f[x]^5)*((1+I*k*f[x])*(2*f[x]^2-3*a^2)+(k*a*f[x])^2)*I*
          d/(2*Pi*w)+p),{x,-d/2,d/2}]



Out[19]=
\!\(\[Integral]\_\(-\(d\/2\)\)\%\(d\/2\)\(Cos[\(\((1 + 2\ n)\)\ \[Pi]\
\
x\)\/d]\ \((p + \(\(1\/\(8\ \[Pi]\^2\ w\ f[x]\^5\)\)\((\[ImaginaryI]\
d\ \
\[ExponentialE]\^\(\(-\[ImaginaryI]\)\ k\ f[x]\)\ \((a\^2\ k\^2\
f[x]\^2 + \
\((1 + \[ImaginaryI]\ k\ f[x])\)\ \((\(-3\)\ a\^2 +
                          2\ f[x]\^2)\))\))\)\))\)\)
\[DifferentialD]x\)

Bye Ben

axlq schrieb:

> I downloaded the trial version of Mathematica to see if it could
> solve a complex integral. After getting comfortable with solving
> simple integrals, I input my target problem:
>
> In[1]:= f[x] = Sqrt[a^2+(q-x)^2]
>
> In[2]:= Integrate[Cos[(2*n + 1)*Pi*x/d]*
>   (Exp[-I*k*f[x]]/(4*Pi*f[x]^5)*((1 + I*k*f[x])*(2*f[x]^2 - 3*a^2)
>     + (k*a*f[x])^2) * I*d/(2*Pi* w) + p), {x, -d/2, d/2}]
>
> Observations:
>
> 1. It's been sitting there for over 24 hours now.
>
> 2. Task Manager shows Mathematica's CPU usage at a constant 50%.
>
> 3. The "Kernel" pull-down menu has "Interrupt Evaluation" grayed out.
>    I can abort it.
>
> 4. Mathematica won't solve any subsequent problem in another window
>    (seems like the first one is occupying a queue).
>
> Earlier I tested some simple function-reference integrals (e.g.
> defining f[x] first and then integrating f[x]dx) and they worked.
>
> What sort of speed can I expect from this?  Is 24 hours too long to
> solve a problem like this on a 2.6 GHz Windows XP platform with 1.25
> GB RAM?  Is Mathematica hung up on something?  Is the fact that I'm
> using the trial version make any difference?  Did I do something
> wrong?
> 
> Thanks.
> -Alex


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