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Numerical Inversion of the Laplace Transform: The Zakian Method

​
a
0
1
a
1
1
a
2
1
This Demonstration shows how to numerically invert the Laplace transform
F(p)
of a simple function
f(t)
:
ℒ(f(t))(p)=F(p)=
1
a
2
2
p
+
a
1
p+
a
0
, where you can set
a
i
for
i=1,2,3
. The magenta curve is the analytical inverse function obtained with the help of the built-in Mathematica function InverseLaplaceTransform and the blue dots are the selected values of the numerical inverse of
F(p)
. It is clear that the Zakian method performs well for this kind of test function.
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