Environmental Engineering Reference
In-Depth Information
Efficiency
Because and are constant for fixed they only
need to be computed once and can be computed to high precision
prior to the start of simulation. Only one matrix multiplication and
one matrix addition are required in each step of simulation. No costly
Newton-Raphson iterations are required. The stepping algorithm is
computationally efficient.
Accuracy
Eq.(4.49) is accurate provided and are computed to
high precision. To ensure a high degree of accuracy, and
should be computed using numerical Laplace inversion of or-
der {
N
,
M
}
=
{8, 10} and fine step size. The followings give an
computationally efficient and yet numerically accurate algorithm that
computes these two quantities over a large number of fine steps.
To compute
to high precision, we first divide
into multiple
fine steps with equal step size
From the definition of
given
in (4.43), we see that the solution of the circuit
at
gives the first column of
Denote the first column of
by
we have
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