discretization

A Dictionary of Computing | 2004 | 700+ words | Copyright

discretization The process of replacing a problem defined on a continuum, say an interval [0,1], by an approximating problem on a finite set of points, say nh, n = 0,1,2,…,N, where h = 1/N

Examples arise in many branches of numerical analysis, principally ordinary and partial differential equations where the finite-difference method and the finite-element method are common forms of discretization. For the ordinary differential equation y′ = f(x,y), 0←x←1, y(0) = y₀,

a simple discretization is given by Euler's method: (1/h)(y_n₊₁ – y_n) = f(x_n,y_n)

where x_n = hn, n = 0,1,…,N, h = 1/N

and y_n denotes the approximation to the true solution y(x) at the point x_n. See also discretization error.

Cite this article
Pick a style below, and copy the text for your bibliography.

MLA
Chicago
APA

JOHN DAINTITH. "discretization." A Dictionary of Computing. 2004. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>.

JOHN DAINTITH. "discretization." A Dictionary of Computing. 2004. Encyclopedia.com. (May 27, 2012). http://www.encyclopedia.com/doc/1O11-discretization.html

JOHN DAINTITH. "discretization." A Dictionary of Computing. 2004. Retrieved May 27, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O11-discretization.html

Learn more about citation styles