Richardson Extrapolation Applied Twice to Accelerate the Convergence of an Estimate
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This Demonstration shows Richardson extrapolation applied twice to accelerate the convergence of an estimate.
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Contributed by: Michail Bozoudis (July 2014)
Suggested by: Michail Boutsikas
Open content licensed under CC BY-NC-SA
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Let be an approximation of the exact value of the integral of that depends on a positive step size with an error formula of the form
,
where the are known constants. For step sizes and ,
To apply Richardson extrapolation twice, multiply the last two equations by and , respectively, and then, by adding all equations, the two error terms of the lowest order disappear:
.
Notice that the approximations and require the same computational effort, yet the errors are and , respectively.
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