alt Hacker NewsThis is what the field of numerical analysis exists for. These details definitely have been treated, but this was done mainly early in the field's history; for example, by people like Wilkinson and Kahan...
This is what the field of numerical analysis exists for. These details definitely have been treated, but this was done mainly early in the field's history; for example, by people like Wilkinson and Kahan...
I just took some basic numerical courses at uni, but every time we discretized a problem with the aim to implement it on a computer, we had to show what the discretization error would lead to, eg numerical dispersion[1] etc, and do stability analysis and such, eg ensure CFL[2] condition held.
So I guess one might want to do a similar exercise to deriving numerical dispersion for example in order to see just how discretizing the diffusion process affects it and the relation to optimal control theory.
[1]: https://en.wikipedia.org/wiki/Numerical_dispersion
[2]: https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%...