Assuming that from some source an approximation of a solution o f (6.9) has been obtained, we calculate

and from the differences

A better approximation is then obtained from

(7.12)

Calculating

and re-evaluating the differences, a still better value is

(7.13)

Generally, a sequence of approximations is obtained recursively from the relation

(7.14)

where . It can be proved that the sequence of numbers thus defined converges for sufficiently small values of to a solution of (7.9) and that this solution is unique.