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Numerical Inversion of the Laplace Transform: The Fourier Series Approximation

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This Demonstration shows how you can numerically compute the inverse of the Laplace transform of a simple function : and . The selected method is the Fourier series approximation. This method uses the following formula in order to perform the inversion of :

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You can select the appropriate values of and that give the correct inverse. This choice must be such that and , where is a measure of the maximum relative error and is the exponential order of .

The red curve is the sine function and the blue dots are the selected numerical values of the inverse of .

You can clearly see how this method may fail to give an accurate inverse if the values of and are not correctly selected. The first snapshot presents a correct inversion result. The next two snapshots show situations where the method gives erroneous data.

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Contributed by: Housam Binous (March 2011)
Open content licensed under CC BY-NC-SA

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R. G. Rice and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, New York: Wiley, 1995.

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