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:
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“The difference between Pound and Whitman is not between the democrat who in deep distress could look hopefully toward the future and the fascist madly in love with the past. It is that between the woodsman and the woodcarver. It is that between the mystic harking back to his vision and the artist whose first allegiance is to his craft, and so to the reality it presents.”
—Babette Deutsch (1895–1982)