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,

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 equationa simple discretization is given by Euler’s method:whereand y_n denotes the approximation to the true solution y(x) at the point x_n. See also discretization error.