# 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.

### Other articles related to "finite difference, finite, finite differences, difference":

Finite Difference in Several Variables
... Finite differences can be considered in more than one variable ... They are analogous to partial derivatives in several variables ...
Hydrogeology - Calculation of Groundwater Flow - Numerical Methods - General Properties of Gridded Methods
... Gridded Methods like finite difference and finite element methods solve the groundwater flow equation by breaking the problem area (domain) into many ... Finite differences are a way of representing continuous differential operators using discrete intervals (Δx and Δt), and the finite difference methods are based on these (they are derived from a Taylor ... time derivative is often approximated using the following forward finite difference, where the subscripts indicate a discrete time location, The ...
Finite Difference Method
... In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to ...
Finite Difference Method - Accuracy and Order
... 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
... The most popular numerical methods used are the finite element, finite difference, and boundary element methods in order of dominance ... In solid mechanics finite element methods are far more prevalent than finite difference methods, whereas in fluid mechanics, thermodynamics, and electromagnetism, finite difference ...

### Famous quotes containing the words difference and/or finite:

If you are really Master of your Fate,
It shouldn’t make any difference to you whether Cleopatra or the Bearded Lady is your mate.
Ogden Nash (1902–1971)

The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.
Blaise Pascal (1623–1662)