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.
Read more about Finite Difference: Forward, Backward, and Central Differences, Relation With Derivatives, Higher-order Differences, Finite Difference Methods, n-th Difference, Newton's Series, Calculus of Finite Differences, Rules For Calculus of Finite Difference Operators, Generalizations, Finite Difference in Several Variables
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