Order of convergence

Definitions

When all the discretizations are generated using a single common method, it is common to discuss the asymptotic rate and order of convergence for the method itself rather than any particular discrete sequences of discretized solutions. In these cases one considers a single abstract discretized solution ${\displaystyle y_{h}}$ generated using the method with a scale parameter ${\displaystyle h}$ and then the method is said to have asymptotic order of convergence${\displaystyle q}$ and asymptotic rate of convergence${\displaystyle \mu }$ if