# Lady Windermere’s Fan (mathematics) | Wikipedia audio article

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 E

( τ

, t ,

y ( t ) ) {\displaystyle E(\ \tau ,t_{0},y(t_{0})\ )}

be the exact solution operator so that: y

( t +

τ )

=E

( τ

, t ,

y ( t )

) y

( t ) {\displaystyle y(t_{0}+\tau )=E(\tau ,t_{0},y(t_{0}))\

y(t_{0})} with t {\displaystyle t_{0}}

denoting the initial time and y

( t

) {\displaystyle y(t)}

the function to be approximated with a given y

( t ) {\displaystyle y(t_{0})}

. Further let y n {\displaystyle y_{n}}

, n

∈ N , n

≤ N {\displaystyle n\in \mathbb {N} ,\ n\leq N}

be the numerical approximation at time t n {\displaystyle t_{n}}

, t