Good reference on matrix-based numerical simulation

[pcoskren]

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

[ted]

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.

[ted]

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.

[sadffg]

what ?i dont know