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# Discretization Definition/Meaning:

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 nth,

n = 0,1,2, ... ,N,

where h = I/N

Examples arise in many branches of numerical analysis, principally ordinary and partial differential equations where the finite-difference method is the common form of discretization. For the ordinary differential equation

y' = ƒ(x,y),

0≤x≤1, y(0) = y0

a simple discretization is given by Euler's method:

(1/h)(yn +1 - yn) = ƒ(xn,yn)

where

xn = hn, n = 0,1, . . . ,N,

h = l/N

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

## Near by Terms:

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