### Solving the voltage of a simple cable WITHOUT Fourier Theory

Posted:

**Mon Dec 07, 2015 11:49 am**Hello,

I hope this is the right place to ask this question. I am intending to use NEURON to teach basic electrophysiology to undergraduate students. However it is unlikely many of them will have "advanced" mathematics coursework by the time they enter my class. I believe I can derive the cable equation with them using only their previous mathematical knowledge in class. I feel it would really be beneficial to show them how a passive cable's voltage really does follow simply from solving this equation in space and time.

I read what I thought were the pertinent chapters of the NEURON book regarding numerical solutions to the equation. The temporal discretization with CN or backwards Euler seems straightforward enough to explain, but the spatial discretization is less obvious. The students (and myself, I confess) do not have enough of a background in Fourier theory to find that analytical solution intuitive. I was trying to figure out a way to solve each spatial dx individually (obviously only for pedagogical purposes) for a given dt.

Simply put, is there a different, perhaps more intuitive way to numerically solve the cable equation

I hope this is the right place to ask this question. I am intending to use NEURON to teach basic electrophysiology to undergraduate students. However it is unlikely many of them will have "advanced" mathematics coursework by the time they enter my class. I believe I can derive the cable equation with them using only their previous mathematical knowledge in class. I feel it would really be beneficial to show them how a passive cable's voltage really does follow simply from solving this equation in space and time.

I read what I thought were the pertinent chapters of the NEURON book regarding numerical solutions to the equation. The temporal discretization with CN or backwards Euler seems straightforward enough to explain, but the spatial discretization is less obvious. The students (and myself, I confess) do not have enough of a background in Fourier theory to find that analytical solution intuitive. I was trying to figure out a way to solve each spatial dx individually (obviously only for pedagogical purposes) for a given dt.

Simply put, is there a different, perhaps more intuitive way to numerically solve the cable equation

**one dx at a time?**