Encyclopedia > Finite difference

  Article Content

Finite difference

There are two subfields of mathematics that concern themselves with finite differences. One is a finite analogue to differential calculus. See also difference operator.

The other is a branch of numerical analysis that aims at approximate solution of partial differential equations. The approach taken by finite difference methods for partial differential equations is to approximate differential operators such as u'(x) by a difference operator such as (u(x+h)-u(x))/h for some small but finite h. Doing this substitution for a large enough number of points in the domain of definition (for instance 0,h,2h,...,1 in the case of the unit interval) gives a system of equations that can be solved algebraically.

The error between this approximate solution and the true solution is determined by the truncation error that is made by going from a differential operator to a difference operator. The term "truncation error" reflects the fact that a difference operator can be viewed as a finite part of the infinite Taylor series of the differential operator.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Wheatley Heights, New York

... County, New York. As of the 2000 census, the town had a total population of 5,013. Geography Wheatley Heights is located at 40°45'43" North, 73°22'1" West ...

This page was created in 23.3 ms