for]_I, + ...

Several centered-space approximations of the convection equation are presented in Sections II A, 11.5, and 11.7.

A characteristic analysis of the wave equation shows that information propagates along two distinct characteristic paths, dx/dt = ±a, in both the positive and negative directions, with the propagation speed a. Since both directions of physical infonnation propagation are implicit in the PDEs, upwind spatial derivative approximations cannot be employed directly. However, centered spatial derivative approximations can be employed, since both forward and backward information are used in the finite difference approximations. This approach is applied to the wave equation in Section 11.9.