Order of accuracy

In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution.Consider u {displaystyle u} , the exact solution to a differential equation in an appropriate normed space ( V , | |   | | ) {displaystyle (V,|| ||)} . Consider a numerical approximation u h {displaystyle u_{h}} , where h {displaystyle h} 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 u h {displaystyle u_{h}} is said to be n {displaystyle n} th-order accurate if the error, E ( h ) := | | u − u h | | {displaystyle E(h):=||u-u_{h}||} is proportional to the step-size h {displaystyle h} to the n {displaystyle n} th power; In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution.Consider u {displaystyle u} , the exact solution to a differential equation in an appropriate normed space ( V , | |   | | ) {displaystyle (V,|| ||)} . Consider a numerical approximation u h {displaystyle u_{h}} , where h {displaystyle h} 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 u h {displaystyle u_{h}} is said to be n {displaystyle n} th-order accurate if the error, E ( h ) := | | u − u h | | {displaystyle E(h):=||u-u_{h}||} is proportional to the step-size h {displaystyle h} to the n {displaystyle n} th power; Where the constant C {displaystyle C} is independent of h and usually depends on the solution u {displaystyle u} .. Using the big O notation an n {displaystyle n} th-order accurate numerical method is notated as