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Finite difference
Discrete analog of a derivative
Finite difference
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly denoted Δ {\displaystyle \Delta } (uppercase Delta), is the operator that maps a function f to the function Δ [ f ] {\displaystyle \Delta [f]} defined by Δ [ f ] ( x ) = f ( x + 1 ) − f ( x ) . {\displaystyle \Delta [f](x)=f(x+1)-f(x).} A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between...
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