Re: Numerical Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg71511] Re: Numerical Integration
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Tue, 21 Nov 2006 07:05:08 -0500 (EST)
- References: <ejrn8h$9a4$1@smc.vnet.net><ejtdna$j3k$1@smc.vnet.net>
Peter I apologize for the situation. My thanks was for you but somehow I confused the names! Best Regards Dimitris dimitris wrote: > Dear David, > > Thanks a lot for your nice solution. > > Here is another along the same lines. > > h[x_] := Tan[BesselJ[0, x]] > > Needs["NumericalMath`BesselZeros`"] > > lst = BesselJZeros[0, 10]; > lst[[0]] = 0; > > f[i_] := NIntegrate[h[x], {x, lst[[i]], lst[[i + 1]]}] > > SequenceLimit[FoldList[Plus, 0, Table[f[i], {i, 0, 9}]]] > 1.45451 > > > Best Regards > Dimitris > > Peter Pein wrote: > > 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