NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 63

The order of Pad é polynomial. When { N, M } = {8, 10} is used,
the corresponding order of integration is M + N + 1 = 19, i.e. the
first 19 terms of the Taylor series expansion of are considered.
The order of integration is hence 18. Numerical Laplace inversion
is thus a high-order numerical integration method.

Because approximates the Taylor series expansion of
at the time origin to minimize the error, the time

displacement from the time origin should be kept small.

The method does not apply to nonlinear circuits simply because it
is generally difficult to obtain the response of nonlinear

circuits.

In what follows we use several examples to demonstrate the effective-
ness and accuracy of numerical Laplace inversion.

A. Dirac Impulse Function

Consider Dirac impulse function The function takes infinite value

at and zero at Because the time-domain value at

is obtained from

When { N, M } = {2, 4} is employed, because when 15 digits are used,
we have This agrees with the theoretical
result. We conclude that numerical Laplace inversion yields the correct