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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