In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution.
, the exact solution to a differential equation in an appropriate normed space
Consider a numerical approximation
is a parameter characterizing the approximation, such as the step size in a finite difference scheme or the diameter of the cells in a finite element method.
The numerical solution
th-order accurate if the error
is proportional to the step-size
th power:[1] where the constant
[2] Using the big O notation an
th-order accurate numerical method is notated as This definition is strictly dependent on the norm used in the space; the choice of such norm is fundamental to estimate the rate of convergence and, in general, all numerical errors correctly.
The size of the error of a first-order accurate approximation is directly proportional to
Partial differential equations which vary over both time and space are said to be accurate to order
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