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

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