Re: Numerical Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg71476] Re: Numerical Integration
- From: Peter Pein <petsie at dordos.net>
- Date: Mon, 20 Nov 2006 06:17:09 -0500 (EST)
- Organization: 1&1 Internet AG
- References: <ejrn8h$9a4$1@smc.vnet.net>
dimitris schrieb: > Dear All, > > I have one question about the numerical integration of one function. > > $VersionNumber > 5.2 > ... > h[x_] := Tan[BesselJ[0, x]] > > Plot[h[x], {x, 0, 40}, PlotPoints -> 100, Axes -> None, Frame -> {True, > True, False, False}, PlotStyle -> AbsoluteThickness[2]] > > Limit[h[x], x -> Infinity] > 0 > > I try hard to find any proper settings for getting a numerical > estimation of its integral > over {0,Infinity} but I can't succeed. > > Any help will be greatly appreciate. > > Dimitris > Hi Dimitris, I tried it this way: In[1]:= Needs["NumericalMath`BesselZeros`"]; h[x_] := Tan[BesselJ[0, x]]; t0 = SessionTime[]; bzlist = NestList[BesselJZerosInterval[0, {1, 2}*Last[#1] + {-1/10, 1/10}] & , Flatten[{0, BesselJZeros[0, 2]}], 9]; v0 = (NIntegrate[h[x], Evaluate[Flatten[{x, #1}]]] & ) /@ bzlist; SequenceLimit[Rest[FoldList[Plus, 0, v0]]] (SessionTime[] - t0)*seconds Out[6]= 1.4545133229307878 Out[7]= 1.75*seconds The displayed result (1.45451) does not change any more when increasing the number of intervals from 9 to 10 or more. Peter