Environmental Engineering Reference
In-Depth Information
In the backward step, the initial condition vector is given by
Substituting (5.39) into (5.40) gives
where
For a fixed and are constant and can be computed in a
pre-processing step before the start of simulation.
can therefore
be computed from
directly.
4. Taylor Series Based Algorithm
It was shown in the preceding section that when inconsistent initial
conditions are encountered at switching instant Dirac impulses
make their appearance only in the step immediately after switching and
do not affect the response in steps thereafter. This observation suggests
that the response of the circuit in the step immediately after switching
can be written in the following form [48]
The first term in (5.43) represents the inconsistent initial conditions at
whereas the second term represents the consistent initial condi-
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