Combining the approximation for the change in storage, Eq. 12, with the respective approximations for net flux into the control interval, Eq. 13, Eq. 14, and Eq. 15, yields:

**Explicit Method:**

**Implicit Method:**

**Midpoint Method:**

The final step in arriving at a finite difference equation that can be used
in a computational setting is to relate the fluxes at and
to the field variable **u**.

First, consider the case that is a constant. Using centered finite difference formulas to approximate the fluxes at the control points and yields

and

with similar formulas for the fluxes at time .