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Discretization error

Quantization error in numerical analysis

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated December 18, 2025

In numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost.

01Examples

Discretization error is the principal source of error in methods of finite differences and the pseudo-spectral method of computational physics.

When we define the derivative of \,\!f(x) as f'(x)=\lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}} or f'(x)\approx {\frac {f(x+h)-f(x)}{h}}, where \,\!h is a finitely small number, the difference between the first formula and this approximation is known as discretization error.

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This article is adapted from the Wikipedia article “Discretization error”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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