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4.2.3 Nordsieck Formulation of the PC Method
Instead of threading a NGB polynomial through preceding points,
expand about .
``Taylor predictor''(e.g. of order 3):
Defining the vector
and the (Pascal triangle) matrix
we have
Now evaluate:
Evaluation step:
Insert
in the force law:
Corrector step:
Define the deviation
and write the corrector as
with an optimized coefficient vector
.
The first few vectors are
Advantages of Nordsieck PC:
- Self-starting
- Adjustable time steps
Stability: Again, between explicit (bad) and implicit (good).
Next: 4.2.4 Runge-Kutta Method for
Up: 4.2 Initial Value Problems
Previous: 4.2.2 Predictor-Corrector Method for
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001