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 method with step width
this would be: 
The local error
is then given by:
![{\displaystyle d_{n}:=D(\ h_{n-1},t_{n-1},y(t_{n-1})\ )\ y_{n-1}:=\left[\Phi (\ h_{n-1},t_{n-1},y(t_{n-1})\ )-E(\ h_{n-1},t_{n-1},y(t_{n-1})\ )\right]\ y_{n-1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a95750df0760038dfd29743092dbf6de1154c7e4)
In abbreviation we write:



Then Lady Windermere's Fan for a function of a single variable
writes as:

with a global error of 
Explanation
![{\displaystyle {\begin{aligned}y_{N}-y(t_{N})&{}=y_{N}-\underbrace {\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})+\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})} _{=0}-y(t_{N})\\&{}=y_{N}-\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})+\underbrace {\sum _{n=0}^{N-1}\ \prod _{j=n}^{N-1}\Phi (h_{j})\ y(t_{n})-\sum _{n=1}^{N}\ \prod _{j=n}^{N-1}\Phi (h_{j})\ y(t_{n})} _{=\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})-\sum _{n=N}^{N}\left[\prod _{j=n}^{N-1}\Phi (h_{j})\right]\ y(t_{n})=\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})-y(t_{N})}\\&{}=\prod _{j=0}^{N-1}\Phi (h_{j})\ y_{0}-\prod _{j=0}^{N-1}\Phi (h_{j})\ y(t_{0})+\sum _{n=1}^{N}\ \prod _{j=n-1}^{N-1}\Phi (h_{j})\ y(t_{n-1})-\sum _{n=1}^{N}\ \prod _{j=n}^{N-1}\Phi (h_{j})\ y(t_{n})\\&{}=\prod _{j=0}^{N-1}\Phi (h_{j})\ (y_{0}-y(t_{0}))+\sum _{n=1}^{N}\ \prod _{j=n}^{N-1}\Phi (h_{j})\left[\Phi (h_{n-1})-E(h_{n-1})\right]\ y(t_{n-1})\\&{}=\prod _{j=0}^{N-1}\Phi (h_{j})\ (y_{0}-y(t_{0}))+\sum _{n=1}^{N}\ \prod _{j=n}^{N-1}\Phi (h_{j})\ d_{n}\end{aligned}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7090de45ea4b48218d99e730704c5dcd186ae1d1)