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3 Material Balance Finite Difference Equations in One Dimension     continued...

Then the integral conservation law Eq. 10 can be written

We next use the midpoint quadrature rule to approximate the left side of Eq. 11. That is:

When developing conservation law FDEs, there are three commonly used strategies for using numerical integration to approximate the integral on the right side of Eq. 11:

Left end-point quadrature:

Right end-point quadrature:

Midpoint quadrature: