Web Reference: Let y = f(x) be a given function of x. Let y 0 , y1,..., yn be the values of y at. x= x0 , x1 , x2 ,..., xn respectively. Then. y1 − y0 = ∇y1. y 2 − y1 = ∇y2. y n − yn−1 = ∇yn. are called the first (backward) differences. The operator ∇ is called backward difference operator and pronounced as nepla. If necessary, the finite difference can be centered about any point by mixing forward, backward, and central differences. Sometimes, the low order derivatives of a function may be analytically known, but high order derivatives are not. The document defines and provides examples of the backward difference operator. The backward difference operator calculates the difference between neighboring values moving in the backward direction.
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