Re: Num. integration problem in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg53826] Re: Num. integration problem in Mathematica
- From: Urijah Kaplan <uak at sas.upenn.edu>
- Date: Fri, 28 Jan 2005 02:44:37 -0500 (EST)
- Organization: University of Pennsylvania
- References: <ctahqm$apt$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Using Mtm 5.1 and making some small changes (don't use floating point values!!!) I received a (hopefully) correct answer. Ma = 10^10; m1 = Rationalize[0.06*10^(-9)]; mPl = Rationalize[1.221*10^19]; v = 174; lambda = Rationalize[0.4]; yt = Rationalize[0.6]; gy = ((1/81)*4*Pi)^(1/2); g2 = ((1/38)*4*Pi)^(1/2); g3 = ((1/26)*4*Pi)^(1/2); mH = ((3/16)*g2^2 + (1/16)*gy^2 + (1/4)*yt^2 + (1/2)*lambda)^(1/2)*Ma; mL = ((3/32)*g2^2 + (1/32)*gy^2)^(1/2)*Ma; mQ = ((1/6)*g3^2 + (3/32)*g2^2 + (1/288)*gy^2 + (1/16)*yt^2)^(1/2)*Ma; mU = ((1/6)*g3^2 + (1/18)*gy^2 + (1/8)*yt^2)^(1/2)*Ma; aH = mH^2/Ma^2; aL = mL^2/Ma^2; aQ = mQ^2/Ma^2; x = s/Ma^2; smin = Max[(mQ + mU)^2, (mL + Ma)^2]; s = smin/y; NIntegrate[ s^(1/2)*BesselK[1, s^(1/2)/Ma]*(3/(4*Pi))*(Ma*m1/v^2)*yt^2*((x - 1 - aL)*(x - 2*aQ)/(x*( x - aH)^2))*(((1 + aL - x)^2 - 4*aL)*(1 - 4*aQ/x))^(1/ 2)*(1/y^2), {y, 0, 1}, MinRecursion -> 10, MaxRecursion -> 50, WorkingPrecision -> 35] 23573.56641066495124896399363987458797535501`25.202227120473328 (`25.202227120473328 means that the answer is given to about 25 digits of precision) --Urijah Kaplan Antonio Cardoso wrote: > Hello, I'm trying to solve this numerical integration in Mathematica: > > Ma = 10^10; > m1 = 0.06*10^(-9); > mPl = 1.221*10^19; > > v = 174; > lambda = 0.4; > yt = 0.6; > gy = ((1/81)*4*Pi)^0.5; > g2 = ((1/38)*4*Pi)^0.5; > g3 = ((1/26)*4*Pi)^0.5; > > mH = ((3/16)*g2^2 + (1/16)*gy^2 + (1/4)*yt^2 + (1/2)*lambda)^0.5*Ma; > mL = ((3/32)*g2^2 + (1/32)*gy^2)^0.5*Ma; > mQ = ((1/6)*g3^2 + (3/32)*g2^2 + (1/288)*gy^2 + (1/16)*yt^2)^0.5*Ma; > mU = ((1/6)*g3^2 + (1/18)*gy^2 + (1/8)*yt^2)^0.5*Ma; > > aH = mH^2/Ma^2; > aL = mL^2/Ma^2; > aQ = mQ^2/Ma^2; > > x = s/Ma^2; > > smin = Max[(mQ + mU)^2, (mL + Ma)^2]; > s = smin/y; > > NIntegrate[s^0.5*BesselK[1,s^0.5/Ma]*(3/(4*Pi))*(Ma*m1/v^2)*yt^2*((x-1-aL)*(x-2*aQ)/(x*(x-aH)^2))*(((1+aL-x)^2-4*aL)*(1-4*aQ/x))^0.5*(1/y^2),{y,0,1},MinRecursion->10,MaxRecursion->35,WorkingPrecision->35] > > but it can't give me the right answer. I't gives the error: > > NIntegrate::slwcon: > Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration being 0, oscillatory integrand, or insufficient WorkingPrecision. If your integrand is oscillatory try using the option Method->Oscillatory in NIntegrate. > > I have already tried to change the options, like WorkingPrecision, PrecisionGoal, SingularityDepth, etc., but it didn't work. > > Can someone help me to solve this problem? > > Thank you, > > Antonio Cardoso