We're not anywhere there yet, but we're closer than we've ever been, and things keep moving in the wrong direction.
We're not anywhere there yet, but we're closer than we've ever been, and things keep moving in the wrong direction.
Deleted Comment
When I read statements like this, I wonder if this is related to optimal policy conditions required for infinitely lived Bellman equations to have global and per-period policies in alignment
Trying to timestep through a constraint that should hold instantaneously creates artificial numerical difficulties. The Bellman equation's value iteration is actually another example of this same pattern...
Trying to handle instantaneous constraints and propagating modes with a single timestepper is often suboptimal.
I developed a framework that systematically separates these components: using direct elliptic solvers for constraints and explicit methods for flux evolution. The resulting algorithms are both more stable and more efficient than unified implicit approaches.
The key insight is that many systems (EM, GR, fluids, quantum mechanics) share the same pattern: - An elliptic constraint equation (solved directly, not timestepped) - A continuity law for charge/mass/probability flux - Wave-like degrees of freedom (handled with explicit methods)
Witgh this structure, you can avoid the stiffness issues entirely rather than trying to power through them with implicit methods.
https://github.com/MidnightBSD/src/commit/7d956a27123f2d77a0...