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, Δf(x) = f(x + h) − f(x) backward difference, Δf(x) = f(x) − f(x − h) central difference, δf(x) = f(x + ½h) − f(x − ½h) Difference equations arise in the application of the finite-difference method.
Δf(x) = f(x + h) − f(x)
Δf(x) = f(x) − f(x − h)
δf(x) = f(x + ½h) − f(x − ½h)