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Innumerical analysis,computational physics, andsimulation,discretization error is theerror resulting from the fact that afunction of acontinuous variable is represented in the computer by a finite number of evaluations, for example, on alattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increasedcomputational cost.
Discretization error is the principal source of error in methods offinite differences and thepseudo-spectral method of computational physics.
When we define the derivative of as or, where is a finitely small number, the difference between the first formula and this approximation is known as discretization error.
Insignal processing, the analog of discretization issampling, and results in no loss if the conditions of thesampling theorem are satisfied, otherwise the resulting error is calledaliasing.
Discretization error, which arises from finite resolution in thedomain, should not be confused withquantization error, which is finite resolution in therange (values), nor inround-off error arising fromfloating-point arithmetic. Discretization error would occur even if it were possible to represent the values exactly and use exact arithmetic – it is the error from representing a function by its values at a discrete set of points, not an error in these values.[1]