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Re: Mathematica freezes?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126996] Re: Mathematica freezes?
  • From: James Stein <mathgroup at stein.org>
  • Date: Fri, 22 Jun 2012 03:03:17 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201206210918.FAA15979@smc.vnet.net>

Does not freeze on my computer (MacBook Pro), but took awhile.
Eventually this answer appeared:
-1.70252*10^-14 - 2.60026*10^-14 i
but along the way produced two messages:

NIntegrate::slwcon: Numerical integration converging too slowly;
suspect one of the following: singularity, value of the integration is
0, highly oscillatory integrand, or WorkingPrecision too small.

NIntegrate::eincr: The global error of the strategy GlobalAdaptive has
increased more than 2000 times. The global error is expected to
decrease monotonically after a number of integrand evaluations.
Suspect one of the following: the working precision is insufficient
for the specified precision goal; the integrand is highly oscillatory
or it is not a (piecewise) smooth function; or the true value of the
integral is 0. Increasing the value of the GlobalAdaptive option
MaxErrorIncreases might lead to a convergent numerical integration.
NIntegrate obtained -1.70252*10^-14-2.60026*10^-14 I and
3.41485808889887`*^-13 for the integral and error estimates.

HTH

On Thu, Jun 21, 2012 at 2:18 AM, Alex Khmelnitsky <akhmel6 at gmail.com> wrote:
> When I try to do the following commands:
>
> r = 3.7; a = 5.1; z = 1.1; p = 0.61;
>
> e = Exp[I f];
> ep = Exp[I p];
> tc = r \[Rho] ep/e;
> l1 =  1/2 (Sqrt[(r + a)^2 + z^2] - Sqrt[(r - a)^2 + z^2]);
> l2 =
>  1/2 (Sqrt[(r + a)^2 + z^2] + Sqrt[(r - a)^2 + z^2]);
> sq = Sqrt[a^2 - \[Rho]^2];
> sq1 = Sqrt[a^2 - l1^2];
> sq2 = Sqrt[ l2^2 - a^2];
> \[Rho] = a Sin[x];
> ff1 =  2 Pi (a^2/(a^2 - tc)^(3/2) ArcTan[Sqrt[a^2 - tc]/sq2] - (
>    tc sq2)/((a^2 - tc) (l2^2 - tc)));
>
> NIntegrate[ff1 \[Rho]^2/e, {f, 0, 2 Pi}, {x, 0, Pi/2}],
>
> it freezes Mathematica. Does it freeze on anyone else's computer?
>
> Thanks.
>



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