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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).

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**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