       animation

• To: mathgroup at smc.vnet.net
• Subject: [mg69761] animation
• From: dimmechan at yahoo.com
• Date: Fri, 22 Sep 2006 01:04:40 -0400 (EDT)

```Dear everyone,

I have the following function

f[x_] := BesselJ[0, x]/Sqrt[(x/10)^2 + 1]

Here is its integral over the range {x,0,infinity}

Timing[Integrate[f[x], {x, 0, Infinity}]]
{4.282*Second, 10*BesselI[0, 5]*BesselK[0, 5]}
a = N[%[]]
1.005450455076402

Here is its numerical estimation with the option
Method->Oscillatory activated.

NIntegrate[f[x], {x, 0, Infinity}, Method -> Oscillatory]
1.005450455076402

Here I define a pure function intframe which give for
different values of the MaxRecursion option the
numerical approximation of the integral, along with the
exact value a, the needing time for the estimation and the
sampled points by NIntegrate.

intframe = Block[{Message}, ListPlot[Reap[NIntegrate[f[x], {x, 0,
Infinity}, MaxRecursion -> #1, EvaluationMonitor :> Sow[x]]][[
2,1]], Axes -> False, Frame -> True, PlotRange -> {{0, 2500}, {0,
15000}},
PlotLabel -> StringJoin["exact: ", ToString[a], ", MaxRecursion: ",
ToString[#1], ", sampled points:",
ToString[Length[Reap[NIntegrate[f[x], {x, 0, Infinity}, MaxRecursion ->
#1, EvaluationMonitor :> Sow[x]]][[2,1]]]],
"\n {time, approximation}: ", ToString[Timing[NIntegrate[f[x], {x, 0,
Infinity}, MaxRecursion -> #1]]]],
ImageSize -> {600, 400}, TextStyle -> {FontFamily -> "Times", FontSize
-> 16},
FrameTicks -> {Automatic, Automatic, None, None}]] & ;

It works fine, as you can see

intframe /@ Range[4, 16,2]

What I need now is to make an animation of this graph.
I define

anframe[n_]:=intframe[n]

and I use

Block[{Message}, Animate[anframe[n], {n, 1, 10,
1}]*SelectionMove[EvaluationNotebook[], All, GeneratedCell]*
FrontEndTokenExecute["OpenCloseGroup"]; Pause[0.1];
FrontEndExecute[{FrontEnd`SelectionAnimate[200, AnimationDisplayTime ->
0.1, AnimationDirection -> ForwardBackward]}]]

(the last command is a slightly modification for my needs of a
command that appeared yesterday on a David's Park post and on
private communacation of myself with him).