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:
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
with similar formulas for the fluxes at time .