Glossary

Richardson extrapolation

Combining two approximations with different steps to cancel the leading error term.

Definition

If $A(h)=A+Ch^p+\mathcal{O}(h^q)$ , the combination $\frac{2^p A(h/2)-A(h)}{2^p-1}$ removes the $h^p$ term and raises the order to $q$ . Applied repeatedly it generates methods such as Romberg integration.

How it is used

It is nearly free accuracy when you already compute with two steps; moreover, comparing $A(h)$ and $A(h/2)$ gives a practical error estimate.