NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 77

It was shown in [5] that for M - N = 2, if numerical
Laplace inversion will yield a stable response. Numerical Laplace
inversion is therefore an absolutely stable (A-stable) numerical inte-
gration algorithm.
4. Summary
In this chapter, we have reviewed the linear single-step predictor-
corrector algorithms and linear multi-step predictor-corrector algorithms,
their imitations in analysis of mixed-mode switching circuits. Numer-
ical Laplace inversion that derives the time domain solution from its
response has been introduced. We have shown that Pad é ap-
proximation based numerical Laplace inversion is a high-order numerical
integration method for linear circuits with accuracy orders of magnitude
higher as compared with LMS-PC algorithms. In addition, we have
shown that this method is capable of handling both impulses and dis-
continuities in network variables that can not be handled by LMS-PC
algorithms. The dependence of the accuracy of numerical Laplace inver-
sion on the time displacement from the time origin has been studied in
detail. For a given function, an optimal step size at which the error is
the minimal, exists. To improve accuracy, we have shown that the step-
ping algorithm with the step size set to the optimal step size can provide
superior numerical accuracy in computing the time domain response of
linear circuits over a time interval of arbitrary length.