Lady Windermere's Fan (mathematics)

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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[edit]

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:

with

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

Explanation[edit]

See also[edit]