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.
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