**Explicit (Forward in Time) Finite Difference Method
[for ]:**

or,

where

For the explicit method Eq. 21
to be stable, **rx** and **ry** must be
restricted to satisfy .
As with the one space variable case, this explicit method provides a
simple computational algorithm that is easy to implement efficiently on
vector and parallel
architectures. However, in many practical problems, its stability restriction often limits
its range of applicability.

If we evaluate the numerical approximations to the flux at time , we obtain the following.