Precision tolerances

[fjebaker]

There's several arbitrarily set precisions in the tests, and more generally some unusually high discrepencies in the values calculated between different methods (see brief mention in this blog post).

We should have a suite of tests that

• ensures the precisions of all methods are known
• attempts to minimize any extraneous errors
• keeps the different integration methods consistent with eachother

I think as an aim, we want our methods to agree within 1e-8 or 1e-9 for relative tolerances. In the literature this isn't really discussed other than occasionally ensuring

$$ g_{\sigma\nu} \dot{u}^\sigma \dot{u}^\nu + \mu^2 < \varepsilon \approx 10^{-8} $$

and even that has a big "-ish" stamped onto the end, as some authors don't even really seem to check that, and others just check whether it agrees with some other simulation.

I think we can do better and quantify the errors more.

[phajy]

There's a typo in the URL. I think you mean this blog post.