to be honest I don't have much experience with the numerical inversion of a Laplace-Transformation and with Mathematica either.
Now I tried that using Mathematica Add-Ons:
http://library.wolfram.com/infocenter/MathSource/2691/, http://library.wolfram.com/infocenter/MathSource/5026/ and http://library.wolfram.com/infocenter/Demos/4738/
If I trie to do that for simple functions e.g.
fun[s_]=(1/s) Exp[-Sqrt[ (s^2 + (37/100) s + 1)/(s^2 + s + Pi)]] the results look quite similar: For T=20
Stehfest[fun[s], s, T] (*From the 1st Add-On*)
GWR[fun, T] (*From the 3rd Add-On*)
Durbin[fun[s], s, T] (*From the 1st Add-On*)
FT[fun, T] (*From the 2nd Add-On*)
The output is:
But now for a function like
fun[s_] = CDF[NormalDistribution[0, 1], s]
the results are:
totally different. Whats the problem here? Do you know other Add-Ons that could work here? I found some other methods here http://library.wolfram.com/infocenter/MathSource/6557/#downloads but the code is not published, isn't it?
Thank you in advanced!