**Implicit (Backward in Time) Finite Difference Method
[for )]:**

which can be written

Since Eq. 17 involves five unknown **U**-values at the time level
, its solution
requires that a system of linear equations be satisfied.
The structure of these linear equations and some techniques for dealing with
these equations are discussed in the next
section.
The implicit method Eq. 17 can be shown to provide a
stable finite
difference scheme for all choices of **rx** and **ry**.

We now turn our attention to the case that the coefficients **c** and
are not constant.
First, we consider the case that **c** and depend explicitly on
**x**, **y**, and **t**.
To facilitate this discussion, consider a grid labeled as indicated in
Figure 3.

Figure 3: Block centered finite difference grid.