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. A numerical solution to a differential equation is said to be n th-order accurate if the error, E , is proportional to the step-size h to the n th power;

The size of the error of a first-order accurate approximation is directly proportional to h . In big O notation, an n th-order accurate numerical method is notated as O ( h n ) . Partial differential equations which vary over both time and space are said to be accurate to order n in time and to order m in space.