Lady Windermere's Fan for a function of one variable
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Let be the exact solution operator so that:
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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:
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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:
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In abbreviation we write:
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Then Lady Windermere's Fan for a function of a single variable writes as:
with a global error of
Explanation
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See also
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