
It is instructive to look at graphs of the discontinuity functions f
1
(x
1
, x
2
) and f
2
(x
1
, x
2
). Figure
6.65 shows their time histories for the conditions listed in Figure 6.59.
The zero crossings of f
1
(x
1
, x
2
) and f
2
(x
1
, x
2
) correspond to the trans itions of the system
between regions S
1
and S
2
. A close-up view of the discontinuity funct ions is shown in Figure 6.66.
Note how the quadratic interpolation function ‘‘INTRP’’ successfully locates the zero crossings,
enabling the RK-4 integrator to stop at the correct point in time within the integration interval, reset
the derivative functions, and then continue to integrate for the remainder of the interval ...