Environmental Engineering Reference
In-Depth Information
As an example, consider the RC network of Fig.4.5 studied earlier.
This time, the stepping algorithm is employed to compute the output
voltage of the network. When the initial condition of the capacitor is
considered, the output voltage in
is given by
As seen in Fig.4.6 that when the step size is
a small error in
the range of
can be achieved. The response of the circuit from
to
is computed with step size
(100 steps).
Assuming that in the first step
The response of the circuit
at
is given by
In the second step, the voltage across the capacitor is given by
and
the response is computed from
In the
step
The relative error of the response computed using the non-stepping al-
gorithm and that using the stepping algorithm are shown in Fig. 4.7.
It is evident that the relative error is significantly reduced at large step
sizes when the stepping algorithm is employed.
In what follows we examine the properties of the stepping algorithm.
Input Waveform
Although in the preceding development, an exponential signal was
used as the input in the derivation of the stepping algorithm, the in-
put waveform is not restricted to be either sinusoidal or exponential.
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