# Numerical Inversion of the Laplace Transform: The Zakian Method

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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.

Contributed by: Housam Binous (March 2011)

Open content licensed under CC BY-NC-SA

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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.

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