Numerical Inversion of the Laplace Transform: The Fourier Series
Approximation 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.