Discretization error

In numerical analysis, computational physics, and simulation, discretization error is 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.

Discretization error should not be confused with round-off error arising from floating point arithmetic. Discretization error would occur even if it were possible to use exact arithmetic.

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 $f\text{'}(x)\; =\; lim\_\{hrightarrow0\}\{frac\{f(x+h)-f(x)\}\{h\}\}$ or $f\text{'}(x)approxfrac\{f(x+h)-f(x)\}\{h\}$, where $,!h$ is a finitely small number, the difference between the first formula and this approximation is known as discretization error.

See also

• Discretization
• Quantization error