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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