  Dendritic processing is now considered to be important in pre-processing of
signals coming into a cell. Dendrites are involved in both propagation and
backpropagation of signals. In a cylindrical dendrite, signals moving in either
direction will be similar. However, if the dendrites taper, then this is not
the case any more. The picture gets more complex if the ion channel
distribution along the dendrite is also non-uniform. These equations have been
solved using the Chebyshev pseudo-spectral method. Here we look at non-uniform
dendritic voltage gated channels in both cylindrical and tapering dendrites.
For back-propagating signals, the signal is accentuated in the case of tapering
dendrites. We assume a Hodgkin-Huxley formulation of ion channels and solve
these equations with the compact finite-difference scheme. The scheme gives
spectral-like spatial resolution while being easier to solve than spectral
methods. We show that the scheme is able to reproduce the results obtained from
spectral methods. The compact difference scheme is widely used to study
turbulence in airflow, however it is being used for the first time in our
laboratory to solve the equations involving transmission of signals in the
brain.
