Environmental Engineering Reference
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small. The use of large step size
although avoiding the effect of Dirac
impulses at
only yields a poor approximation of
simply be-
cause the time point
is distance away from the switching instant
It was shown in [47] that this difficulty can be overcome by first taking
a large forward step from to where As long as is
sufficiently large, the effect of Dirac impulse at dies out and the
result obtained at has good accuracy (in this example, ).
Note that the function must be continuous at This ensures
Second, a backward step of the same size is taken from
to the circuit in this case has no input nor its response
has a Dirac impulse. The capacitor, however, carries the initial voltage
as shown in Fig.5.1. The output voltage of the circuit in this step
is given by
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