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In [[numerical analysis]], '''order of accuracy''' quantifies the [[rate of convergence]] of a numerical approximation of a [[differential equation]] to the exact solution. A numerical solution to a differential equation is said to be '''<math>n</math>th-order accurate''' if the error, <math>E</math>, is proportional to the step-size <math>h</math> to the <math>n</math>th power;<ref name="LeVeque">{{cite book|last=LeVeque|first=Randall J|title=Finite Difference Methods for Differential Equations|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.1693|year=2006|publisher=University of Washington|pages=3–5}}</ref>

:<math> E(h) = Ch^n </math>

The size of the error of a first-order accurate approximation is directly proportional to <math>h</math>. In [[big O notation]], an <math>n</math>th-order accurate numerical method is notated as <math>O(h^n)</math>. [[Partial differential equations]] which vary over both time and space are said to be accurate to order <math>n</math> in time and to order <math>m</math> in space.<ref name="Strikwerda">{{cite book|last=Strikwerda|first=John C|title=Finite Difference Schemes and Partial Differential Equations|edition=2|year=2004|isbn=978-0-898716-39-9|pages=62–66}}</ref>

The order of accuracy of several numerical methods are given below.

{| class="wikitable"
|-
! Method
! Order of accuracy
|-
| [[Finite difference|Forward difference, backward difference]]
| <center><math>O(h)</math></center>
|-
| [[Central difference]]
| <center><math>O(h^2)</math></center>
|-
| [[Runge–Kutta methods#Common fourth-order Runge–Kutta method|Fourth-order Runge–Kutta method]]
| <center><math>O(h^4)</math></center>
|}

== References ==
{{reflist}}

[[Category:Numerical analysis]]

{{math-stub}}

Steinberg formula - Revision history

en>Mark viking: Added wl