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. >

**References**:**Mathematica freezes?***From:*Alex Khmelnitsky <akhmel6@gmail.com>