Extracting derivatives (du/dt) from an ODE problem

I see, that explains it.
I am going to take a look what is going on in here! it’s not very clear for me (I’m a rookie after all!)
However now I know what the problem was. Thank you

It’s not too difficult. Essentially the interpolation is just an interpolation in Θ. So that’s basically 24*r014 + 120*r015*Θ + 360*r016*Θ^2 + ... is the polynomial for the 4th derivative in time at t + Θ*dt. So then the 5th derivative is just the derivative of that polynomial and divide by another dt, so then you’d drop down the powers and etc. etc.

The way we have it written out will get it done, but it’s just tedious to add the next ones. However, to get it done today, we might as well get a PR that writes out the next orders and just merge it.

How hard would it be to do this via metaprogramming? Which defines lots of higher order derivatives?

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Yes. Can this be automated? or would that come with a hefty performance hit? since I am assuming right now, it just jumps into the required order without extra computation.

Metaprogramming won’t have a performance hit, someone just has to do it. How hard? Who knows. Someone has to try it first.