Environmental Engineering Reference
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results of Dirac impulse function.
B. Unit Step Function
The unit step function is defined as
Its Laplace transform is given by
Using numerical Laplace
inversion, its time-domain value at
with {
N, M
}
=
{2, 4} is ob-
tained from
The relative error defined as
with is plotted in Fig.4.3. It is seen that numerical Laplace
inversion yields the accurate results of
even for large step sizes. The
error is in the range of
C. Exponentially Decaying Function
The exponentially decaying function,
represents the charac-
teristics of RC networks. Because
its time-domain response at
with {
N, M
}
=
{2, 4} can be com-
puted from
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