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3.1 FDEs with Variable Coefficients     continued...

Case 2---c and depend on : In this case, if we return to the integral conservation law, Eq. 10, and proceed with similar arguments as in the constant coefficient case, we obtain an explicit FDE of the form

where

Unless the coefficient of the term is ``lagged,'' by replacing by , the left side of this FDE will contain nonlinear terms involving and will not be algebraically explicit in a computational sense. Such lagging of nonlinearities is a common technique in computations.

Since the solution to the FDE is not known at the points and , other methods for setting the -value at these points must be used. Three commonly used techniques are

Arithmetic Average

Geometric Average

Harmonic Average