🚀 go-pugleaf

My numerical integration prof just walked us through advective systems
last night (a 3-hour lecture delivered in 2.5 hours--my mental digestive
processes are still churning). He discussed the practical limitations on
the various integration schemes:

Central difference in space, forward euler in time: tends to have
monotonicity problems. Stochastic resonance processes in neural systems
would not do well with this scheme.

First order upwind: conditionally stable, but diffusion occurs. Neurons
are known to show hyperacuity in some contexts by detecting the tight
synchronization of inputs. This scheme would have problems doing that.

Lax-Wendroff: conditionally stable but non-monotonic. Again, problems in
the context of stochastic resonance.

Flux-corrected transport: fully conservative and preserves monotonicity.
I would expect problems though with distributed synchronization of
neurons.

I'm beginning to get the impression that current PDE schemes can be
expected to find the aspects of neuron dynamics that I'm interested in
'at the bleeding edge.' Godunov's theorem seems to imply that an
accurate neural system model has to make use of non-linear schemes.

--
Harry Erwin
Internet: herwin@gmu.edu 
Just a dumb graduate student working on Katchalsky network models....
(And if you believe that, I have a ranch in California to sell you.)