www.neuron.yale.edu

I am new in NEURON and I am trying to find out in which file does the membrane potential (v) has its expression ( the differential equation that is used probably). I would highly appreciate if someone could provide me that voltage equation that NEURON is using and the file_name that it is in the documents.
Thank you in advance

Good question. There is no such file. Creating a section gives you the spatially discretized cable equation with no ionic membrane current, i.e. a charge balance equation that states
capacitive membrane current in a compartment = net current entering the compartment from adjacent compartments
but you don't see the equation--NEURON sets up internal data structures that represent it. You add membrane ionic currents by adding one or more "mechanisms" into a section. A "mechanism" is basically a bag of equations that describe the properties of a membrane current--what ionic species carries the current, the time-, voltage-, and ligand-dependence of the dynamics of the conductance through which the current flows. But the syntax for adding a mechanism does not involve those equations. Instead, the description of a mechanism is written in a programming language called NMODL and saved to a file which is then compiled to produce a library that NEURON loads when it starts.

You might find it helpful to read
https://neuron.yale.edu/neuron/static/p ... /nctoc.htm
(you might prefer to download the pdf)
and
https://neuron.yale.edu/neuron/static/p ... /nmodl.htm

Dear ted,

Thank you for your detailed answer.