discretization
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)(yn+1 – yn) = f(xn,yn)
where xn = hn, n = 0,1,…,N, h = 1/N
and yn denotes the approximation to the true solution y(x) at the point xn. See also discretization error.
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)(yn+1 – yn) = f(xn,yn)
where xn = hn, n = 0,1,…,N, h = 1/N
and yn denotes the approximation to the true solution y(x) at the point xn. See also discretization error.
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discretization