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.
The Zakian method uses the following formula in order to invert : , where and are the tabulated constants for the Zakian method.
R. G. Rice and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, New York: Wiley, 1995.