Environmental Engineering Reference
In-Depth Information
The above equation reveals that in order to have a stable numerical
solution, the step size
must be such that
is outside the unit circle
centered at (1,0), as shown in Fig.4.1.
It should be noted that if i.e. the system itself is unstable,
if the step size is chosen such that the response computed
from backward Euler formula will, however, be stable. We conclude from
the preceding analysis that:
Forward Euler formula could yield an erroneous diverging response
for a stable system.
Backward Euler formula could provide a false converging response for
an unstable system.
2. Linear Multi-Step Predictor-Corrector
Algorithms
The linear single-step predictor-corrector algorithms suffer from both
the poor accuracy and the lack of computational efficiency due to the
following reasons:
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