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High Quality Content by WIKIPEDIA articles! In mathematics, to approximate a derivative to an arbitrary order of accuracy, it is possible to use the finite difference. A finite difference can be central, forward or backward. 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. Recurrence relations can be written as difference equations by replacing iteration notation with finite differences.