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

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.