Environmental Engineering Reference
In-Depth Information
It is seen that the response of the circuit is In step 1, the circuit is depicted
by (6.A.10) and its time domain response is given by
In step 2, the time origin is reset to
and the circuit is represented by
It can be shown that at
Continuing this process one obtain
Notice that in computing
and
numerical Laplace inversion is
performed in the first step only. Once
and
are
available,
and
can be computed efficiently and accurately in a
recursive manner.
APPENDIX 6.B: Computation of Parameter Deriva-
tives of and
It was shown in Chapter 4 that and can be computed using multi-
step numerical Laplace inversion to high precision as follows
and
relates to
by
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