> analytic everywhere and when this hypothesis doesn’t hold, the method will just silently fail and return garbage such as infinity or NaN for the.
This method will produce false results and not fail if the right hand side is not analytic but infinitely differentiable. It will also silently fail depending on the implementation of the automatic differentiation in the presence of integrated discontinuities anywhere in the function.
I could be misunderstanding but it may also produce a series that converges, but poorly. When using Taylor series to solve differential equations, there's a final step of "try and recognize the function," so that you can have sin(x) instead of a power series that will take a billion terms to reasonably compute sin(100).
This method will produce false results and not fail if the right hand side is not analytic but infinitely differentiable. It will also silently fail depending on the implementation of the automatic differentiation in the presence of integrated discontinuities anywhere in the function.