The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the step size). The function can then be fitted and evaluated
at 
to yield very accurate results. Press et al. (1992) describe this process
as turning lead into gold. Richardson extrapolation is one of the key ideas used
in the popular and robust Bulirsch-Stoer
algorithm of solving ordinary differential
equations.
Richardson Extrapolation
See also
Bulirsch-Stoer AlgorithmExplore with Wolfram|Alpha
References
Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., p. 106, 1990.Jeffreys, H. and Jeffreys, B. S. "L. F. Richardson's Method." §9.091 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 288, 1988.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Richardson Extrapolation and the Bulirsch-Stoer Method." §16.4 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 718-725, 1992.Referenced on Wolfram|Alpha
Richardson ExtrapolationCite this as:
Weisstein, Eric W. "Richardson Extrapolation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RichardsonExtrapolation.html