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:
“Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very finite and fixed creature, I call the classical.”
—Thomas Ernest Hulme (1883–1917)
“... [woman suffrage] has made little difference beyond doubling the number of voters. There is no woman’s vote as such. They divide up just about as men do.”
—Alice Roosevelt Longworth (1884–1980)