Lady Windermere's Fan (mathematics)
In mathematics, Lady Windermere's Fan is a telescopic identity employed to relate global and local error of a numerical algorithm. The name is derived from Oscar Wilde's play Lady Windermere's Fan, A Play About a Good Woman.
Lady Windermere's Fan for a function of one variable
Let be the exact solution operator so that:
with denoting the initial time and the function to be approximated with a given .
Further let , be the numerical approximation at time , . can be attained by means of the approximation operator so that:
The approximation operator represents the numerical scheme used. For a simple explicit forward euler scheme with step witdth this would be:
The local error is then given by:
In abbreviation we write:
Then Lady Windermere's Fan for a function of a single variable writes as:
with a global error of