NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 67

mately The error, however, increases drastically when the step
size is large. Also observed is that an optimal step size exists. The large
relative error when is small is mainly due to The large error
when is large, however, is due to the large time displacement from the
time origin.
3.3 Multi-Step Numerical Laplace Inversion
Because numerical Laplace inversion is based on Pad é approximation
of in the vicinity of the time origin, its accuracy deteriorates if the time
point has a large displacement from the time origin, as observed in the
preceding section. Practical applications usually require the time domain
behavior of circuits over a long period of time, Eq.(4.31) therefore can
not be applied directly.
An effective way to reduce the error due to a large time displacement
from the time origin is to divide the long time interval into multiple small
sub-intervals of equal width such that the results obtained from numer-