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##

4.2.2 Predictor-Corrector Method for 2nd order ODE

*Predictor step:*

In
replace the function
by a NGB polynomial and integrate twice.

A specific predictor of order is found by using terms up to order
. Thus the predictor of third order reads

For a compact notation we define the vector

and the coefficient vectors
and
. Then

The first few vectors
are given by

*Evaluation step:*

Insert the preliminary result
in the
physical law for :

*Corrector step:*

Insert in a NGB formula centered
on and re-integrate twice:

Defining the vector

and coefficient vectors
, we write

The first few coefficient vectors are

** Next:** 4.2.3 Nordsieck Formulation of
**Up:** 4.2 Initial Value Problems
** Previous:** 4.2.1 Verlet Method
* Franz J. Vesely Oct 2005*

See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001