First, I have this two functions
fun1[x_] = Assuming[x > 0 && x ≤ 1, 0.5((Log[x/2])^2 - (ArcTanh[Sqrt[1 - x^2]])^2)]
and
fun2[x_] = Assuming[x > 1, 0.5((Log[x/2]^2 + (ArcTan[Sqrt[x^2 - 1]])^2)]
both function define a new piecewise function
funtot[x_] = Piecewise[{{fun1[x], x > 0 && x < 1}, {fun2[x], x > 1}}]
I need to define this last function because a I needed in this next numeric integral
F1[y_?NumericQ, w_?NumericQ, g_?NumericQ] := -I * w * Exp[0.5 * w * y^2] *
NIntegrate[x*(BesselJ[0, w * x * y])* Exp[I * w * (0.5 * x^2 - funtot[x] +
0.0243401)],
{x, 0.001, g}, WorkingPrecision → 16, MaxRecursion → 30,
Method → {GlobalAdaptive, MaxErrorIncreases → 10 000}]
as you can see its a complex function, with "y", "w" and "g" parameters. Now with the next order can I create a table called tabreal1 with y = 0.1, g = 0.9999 and w runing on the interval (0.001,100) in steps size of 0.01
tabreal1 = Table[{w, Abs[F1[0.1, w, 0.9999]]}, {w, 0.001, 100, 0.01}]
Mathematica, as you can see in the next image, show me the table tabreal1 in this way because is too big (almost ten thousend couple values), and take almost like one hour
with the next algoritm, Mathematica take the table tabreal1 and plot that table in a LogLogPlot
NFW1b = ListLogLogPlot[tabreal1, Frame->True, PlotRange->{{0.001, 100},
{.25, 10}},
AspectRatio->1, ImageSize->Large, FrameTicks->All,
GridLines->Automatic, PlotStyle->Black, PlotMarkers->{Automatic, 2}]
seconds later, this is the plot
There is some way to create that plot in real time as the table tabreal1 is created? thats it, as Mathematica found some $(w_{1},F1_{1})$ Mathematica puts it immediately in the graph and I can see it, and seconds later when Mathematica found another $(w_{2},F1_{2})$ value Mathematica put in the graph and so on...
I need to require this because I need to make the step size of w smaller, actually with the step size of 0.001 the time taken to do tabreal1 was almost ten hours, I guess with the visual aspect as the graph is crated can figure how time is remaining.
According to Wolfram Documentation center, the command Dynamic can help me to do this, but not work at all.
Thanks in advance for any help.