The one dimensional wave equation with a homogeneous
velocity function has an analytic solution [22].
The wave propagates in two directions; solutions are of the
form 
.
The method
of characteristics can be used to formulate this
analytic solution.
The numerical solution
[10] has the
advantage
of solving the inhomogeneous problem, which is
awkward analytically
but feasible in one dimension.
After mastering the requirements
of one dimensional modeling, the extensions required
for two and three dimensional models are not difficult.
Inhomogeneous modeling in two and three dimensions
requires a numerical method; analytic methods are
not capable of modeling most complex media.
