We've seen errors appearing on different time scales.
The LTE, the local truncation error, that happens at each time step.
There is one more time scale that when they look into mainly what happens in the long run,
what happens if this system runs for 1,000 years, 10,000 years for the age of the universe,
is this solution going to explode or to implode in the long run or will it stick close to the exact solution.
The GTE for one final time does not tell us much about that form.
One way of looking at the long-term error is for instance to look at energy.
If the systems is such that energy should be conserved, we can look at the long-term evolution
of energy to learn whether there is an issue.