Variable Step Size NBody ODE Integration Methods
June 9, 1996
42
Since the RungeKutta method takes several trial points into the future, it is possi
ble to get a crude estimate of the error by looking at the differences between the evaluation
of
f()
at these points. For the standard 4
th
order RungeKutta method, one reference
(11)
states that
is a good estimate for when to change the step size.
For the GraggBulirschStoer method, it is common to keep increasing the number
of steps until a good rational approximation can be obtained.
k
2
k
3

k
1
k
2

0.02
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