How do I numerically compare the Dymos solution to the simulated solution?

For some of the testing we have an assert_timeseries_near_equal function that treats the more dense time series as the truth and tests that the less dense timeseries (usually the discrete solution) is reasonably close to it.

We're actually working on this method a bit more explicit right now so it's a little easier for users to apply in general cases, such as comparing discrete solutions from two different cases.

In general, there's a few different ways you can test your explicit results against an explicit integration. You could just verify that the final states of the two solutions are reasonably close. Since the error tends to increase over the course of the trajectory this is often good enough for a quick check. The downside of this approach is that it doesn't test that both solutions took the same path to the final condition.

To test the solution away from the nodes I'd recommend the following: Add a second timeseries output to the relevant phase that contains more segments or higher order segments. This timeseries will have more nodes. Dymos will interpolate from the solution's collocation grid onto this more dense timeseries output grid. Comparing this against the explicit simulation should still match exactly in terms of times, controls, and parameters, you'll better capture the interpolating state polynomials vs the explicitly simulated results.

There are other statistical methods out there for comparing timeseries that you can bring to bear, but visualizing the explicit trajectory plus some error bound as a "tube" into which we want to fit the discrete solution is usually how I handle it.