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Let A(h) be an approximation of A that depends on a positive step size h with an error formula of the form

where the ai are unknown constants and the ki are known constants such that hki > hki+1.

The exact value sought can be given by

which can be simplified with Big O notation to be

Using the step sizes h and h / t for some t, the two formulas for A are:

Multiplying the second equation by t<sup>k<sub>0</sub></sup> and subtracting the first equation gives

which can be solved for A to give

By this process, we have achieved a better approximation of A by subtracting the largest term in the error which was O(hk0).  This process can be repéated to remove more error terms to get even better approximations.

A general recurrence relation can be defined for the approximations by