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