Re: NIntegrate and Plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg95894] Re: NIntegrate and Plot*From*: dimitris <dimmechan at yahoo.com>*Date*: Thu, 29 Jan 2009 05:56:10 -0500 (EST)*References*: <glethi$4pp$1@smc.vnet.net> <glpfm5$ktq$1@smc.vnet.net>

On 28 =C9=E1=ED, 13:31, mark mcclure <mcmcc... at unca.edu> wrote: > On Jan 24, 6:20 am, dimitris <dimmec... at yahoo.com> wrote: > > > How can I achieve better performance in the following task > > Plot[NIntegrate[fun[r, t], {t, 0, Infinity}], {r, 0, 3}] > > [... Given a complicated fun ....] > > First, I think it will help if you limit the number of > sample points. Plot generates many more sample points > than necessary to view this particular graph. Second, > you might want to deal with the potential numerical > inaccuracies when r is small. Both of these objectives > are easily met using a Table to generate a reasonable > amount of discrete data that you can then ListPlot. The > following takes about 15 seconds on my machine and > generates no complaints. > > fun[r_,t_]= -(((-3 + 4t^2 + 8t^4 - 8t^3 Sqrt[1+t^2])* > BesselJ[1, r*t])/(3 + 14*t^2 + 24*t^4 + 16*t^6 - > 16*t^3*Sqrt[1 + t^2] - 16*t^5*Sqrt[1 + t^2])); > rBigData=Table[{r, NIntegrate[fun[r,t],{t,0,Infinity}]}, > {r, 3/10, 3, 1/10}]; > rSmallData=Table[{r,NIntegrate[fun[r,t],{t,0,Infinity}, > WorkingPrecision -> 20]}, {r, 1/20, 1/4, 1/10}]; > data = Join[{{0, 0}}, rSmallData, rBigData]; > ListLinePlot[data] > > By comparison, your original Plot command took just > over 3 minutes to generate a graph with 307 points that > did not look much better. > > Mark McClure Thank you very much. Best Regards Dimitris