Finite Difference

A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a finite difference is divided by ba, 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 DifferenceForward, Backward, and Central Differences, Relation With Derivatives, Higher-order Differences, Finite Difference Methods, difference">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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Finite Difference in Several Variables
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... See also Finite difference coefficients The error in a method's solution is defined as the difference between its approximation and the exact analytical solution ... The two sources of error in finite difference methods are round-off error, the loss of precision due to computer rounding of decimal quantities, and truncation error or discretization error, the difference between ... To use a finite difference method to attempt to solve (or, more generally, approximate the solution to) a problem, one must first discretize the problem's domain ...
Computational Mechanics - Overview
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