Richardson extrapolation

The Richardson's extrapolation is a numerical analysis technique for estimating the error in the solution by solving the problem with two different grid sizes, provided the functional form of the solution is known.

1. What is Richardson extrapolation formula?
2. What is Richardson extrapolation used for?
3. Why is Richardson extrapolation more accurate?
4. How is Richardson extrapolation applied to integration?

What is Richardson extrapolation formula?

f′(x) = f(x + h) − f(x − h) 2h − h2 6 f′′′(x0) − h4 120 f(5)(x0) −··· . This formula describes precisely how the error behaves. This information can be exploited to improve the quality of the numerical solution without ever knowing f′′′,f(5),.... Recall that we have a O(h2) approximation.

What is Richardson extrapolation used for?

Usually Richardson's extrapolation process is used to improve the order of a formula which approximate a given quantity [1], [2].

Why is Richardson extrapolation more accurate?

In a sense, Richardson extrapolation is similar in spirit to Aitken's ∆2 method, as both methods use assumptions about the convergence of a sequence of approximations to “solve” for the exact solution, resulting in a more accurate method of computing approximations.

How is Richardson extrapolation applied to integration?

Extrapolation is to use known values to project a value outside of the intended range of the previous values. Using the concept of Richardson Extrapolation, very higher order integration can be achieved using only a series of values from Trapezoidal Rule.