Conceptually, a first order hyperbolic wave equation is the simplest wave
propagation model. The characteristic solution [20]
in the time-space
domain for the homogeneous, constant velocity model is illustrated in
Figure 2.
The first order hyperbolic system,
Equation 2, has an analytic solution, 
.
The initial condition is 
and the
slope of the characteristic solution is the media velocity 
.
The sign of 
,
of Equation 2
determines the propagation direction
of the wave. If 
is positive, the
wave propagates to the right. Bidirectional waves are a property
of the
second order hyperbolic wave equation.
To develop a non-reflecting boundary condition,
Reynolds [18]
used first order systems similar to Equation
2. This method of Reynolds is presented in
Section 15.
