This error estimate is very convenient for adaptive stepsize integration algorithms.

The error estimate for a function of regularity is:

The following error estimate shows that linear interpolation is not very precise.

The result and its error estimate are based on a weighted average of independent samples.

The internal model's estimate is also compared to the produced sound to generate an error estimate.

The error estimate is used to correct the internal model.

This local error estimate is third order accurate.

If , we consider the step successful, and the error estimate is used to improve the solution:

A number of different sufficient conditions for the approximations to converge and presents error estimates were given.

The error estimate is used to control the stepsize.