
In reality, c in Equation 6.147 and the two occurrences of c in Equation 6.148 are different and
depend on the derivative function and the intervals; however, for suitably small T, the differences
are negligible. Eliminating e
T
from Equations 6.146 and 6.148 gives
x
A
(i þ 1jT) þ 16e
T=2
¼ x
A
i þ 1
T
2
þ e
T=2
(6:149)
Solving for e
T=2
in Equation 6.149 gives
e
T=2
¼
x
A
i þ 1
T
2
x
A
(i þ 1jT)
15
(6:150)
e
T=2
in Equation 6.150 is an estimate of the local truncation error of the RK-4 integrator when
the step size is T=2. It can be used to adjust the step size in subsequent calculations. For example,
Table 6.5 shows a possible approach to step size adjustment