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.
Discretization error is the principal source of error in methods of finite differences and the pseudo-spectral method of computational physics.
is a finitely small number, the difference between the first formula and this approximation is known as discretization error.
In signal processing, the analog of discretization is sampling, and results in no loss if the conditions of the sampling theorem are satisfied, otherwise the resulting error is called aliasing.