# Numerical Inversion of the Laplace Transform: The Zakian Method

Numerical Inversion of the Laplace Transform: The Zakian Method

This Demonstration shows how to numerically invert the Laplace transform of a simple function : , where you can set for . 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 . It is clear that the Zakian method performs well for this kind of test function.

F(p)

f(t)

ℒ(f(t))(p)=F(p)=+p+

1

a

2

2

p

a

1

a

0

a

i

i=1,2,3

F(p)