I've been trying to learn more about the implementation of NEURON, so far working through the discretization of the neuron and relevant equations to have second order accuracy in space and time. The cables were easy to prove second order accuracy with using Taylor's Theorem, The NEURON Book, and "Efficient Computation of Branched Nerve Equations"(Hines 1983), but I'm stumped at the branch points. I just don't know how to center difference with more than two adjacent compartments. Any help would be greatly appreciated. So far I've read all the numerical and digital considerations in The NEURON Book, but I haven't finished the other parts yet, and I have a pretty good math background. Also, I would like to verify that the reason there is a single and not double partial derivative with respect to x on the left hand side of the main branch equation for conservation of charge is because the branch node is taken to have zero area, as it says in The NEURON Book on page 97. This doesn't make perfect sense to me either since node area is also in the equation.

Thank you for your time.

Mitchal Dichter