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Pick a function f(t) and a starting set of time points t1 which is unevenly spaced.
At 100 evenly spaced points (make sure they aren't on the grid of known values), calculate the mean squared error between the interpolant and f(t).
Refine to t2 which is t1 and each half point.
Calculate the error at the same 100 evenly spaced points
Repeat N times (user chosen)
Use the log approximation to determine the order of convergence. Return a ConvergenceSimulation from DiffEqDevTools.
This should probably just be ConvergenceSimulation so that all of the plots and such are done. This error estimator would be an L2 error approximation.
We need a way to test that the order of accuracy is correct.
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