A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. Today, the term "finite difference" is often taken as synonymous with finite difference approximations of derivatives, especially...