# 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

## Snapshots

## Details

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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