Discretization error

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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.

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

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