Difference Equations Definition/Meaning:

Equations that have the same general form as recurrence relations; however, the term also refers to situations in which the solution is not determined recursively from initial conditions. Difference equations play a large part in numerical computation. The equations are sometimes expressed in terms of differences of function values rather than function values themselves. The standard difference representations are:

forward difference,

Dƒ(x) = ƒ(x + h) - ƒ(x)

backward difference,

у(x) = ƒ(x) - ƒ (x - h)

central/ difference,
 

¶ƒ(x) = ƒ(x + 1/2h) - ƒ(x - 1/2h)

Difference equations arise in the application of the finite difference method.

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