The prototype of a hyperbolic PDE, the linear advection equation (63),
can be discretized
for discrete timesteps
on a spatial grid

(88) 

(89) 
by replacing

(90) 

(91) 
The result is the
explicit Euler scheme
(``naive'' scheme,
FTCS scheme)

(92) 
This looks quite similar to the discretization of the heat equation (85).