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
:
.
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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