  Dendrites have voltage-gated ion channels which aid in production of action
potentials. Thus dendrites are not just passive conductors of information, but
actively act on the incoming input. Here we assume Hodgkin-Huxley formulations
of voltage-gated ion channels on the dendrite. These equations are normally
solved by some form of central difference scheme or the spectral methods. We
use a compact finite-difference scheme to solve these equations. This scheme
gives spectral-like spatial resolution while being easier to solve than
spectral methods. The scheme has shown to be able to reproduce the results from
spectral methods. In this paper cylindrical dendrites are described. It may
also be noted that the compact difference scheme can be used to solve any other
PDE both in biological as well as non biological systems. It is increasingly
used in studying turbulence in airflow.
