Variable Step Size N-Body ODE Integration Methods
June 9, 1996
42
3.4 Method of Internal Checking
Since the Runge-Kutta 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 Runge-Kutta method, one reference
(11)
states that
is a good estimate for when to change the step size.
For the Gragg-Bulirsch-Stoer 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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