facusapienza21
commented
5 months ago Thank you so much @olivierbonte for pointing this out. Yes, indeed there is a mistake in the original calculation, missing two terms here. This is the correct formula:
You didn't miss anything, I did ;)
olivierbonte
When I apply the multivariate Taylor approximation on the first part on equation 63 (section 3.9.4), I get: $u^{t+1} + s^{t+1}\epsilon = u^t + s^t \epsilon + \Delta t f (u^t + s^t \, \epsilon, \theta + \epsilon, t) = u^t + s^t \epsilon + \Delta t (f(u^t,\theta,t) + \frac{\partial f}{\partial u}s^t \epsilon + \frac{\partial f}{\partial \theta}\epsilon)$ In the paper however we get: $u^t + f(u^t,\theta,t) + \Delta t(\frac{\partial f}{\partial u}s^t + \frac{\partial f}{\partial \theta})\epsilon$ So I was wondering here how or why the $\Delta t$ before $f(u^t,\theta,t)$ went out and why $s^t \epsilon$ is dropped. Maybe I am missing something (obvious) here, so feel free to point out any mistake in my reasoning above.