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
Famous quotes containing the words finite and/or difference:
“Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.”
—Elizabeth Fishel (20th century)
“Friends serve central functions for children that parents do not, and they play a critical role in shaping children’s social skills and their sense of identity. . . . The difference between a child with close friendships and a child who wants to make friends but is unable to can be the difference between a child who is happy and a child who is distressed in one large area of life.”
—Zick Rubin (20th century)