www.neuron.yale.edu

Hi,

I'm spending my subway time lately rummaging around through NEURON's source to see what I can learn. Looking through solve.c, I've quickly become disoriented, and I think the problem is that I don't have a solid enough understanding of the numerical methods involved. I understand that for each node of the neuron, a current balance equation is created, discretized according to a Crank-Nicolson formulation, combined with the rest of the current balance equations into a large matrix that is roughly diagonal (with far off-diagonal elements at branch points), and then this is passed to a matrix-solving library to calculate the next time step.

But my understanding is shallow. I've read the papers on the NEURON site, but I'm looking for more. Can somebody suggest a good reference, preferably a textbook, on numerical methods that spends a good chunk of time on using matrices to numerically solve large systems of partial differential equations? Something that's geared toward an engineering, rather than a mathematical, audience would be ideal.

Thanks in advance,
-Patrick

NEURON doesn't solve PDEs, it discretizes them and then solves a family of
ODEs. After discretization, the problem is quite similar to numerical simulation
of an electronic circuit, so any good book on that topic should have what you
need.

This is my favorite book on the subject:
Vlach, J., and Singhal, K.
Computer Methods for Circuit Analysis and Design
Wiley, 1983

On amazon.com I see that it is now published by Van Nostrand Reinhold and
lists for $215 (ouch!), but used copies are available and well worth the price.

what ?i dont know