An integral-interpolatory iterative method for the solution of non-linear scalar equations

This paper deals with the iterative solution of non-linear equations f(x) = 0. We consider integral information on f which is given by f(x Q),f•(x Q),...,f ( s ) ( X q) and J°f(t)dt. We define an intery polatory-integral method which uses integral information and which has maximal order of convergence equal to s+3. Since the maximal order of iterations which use f ( x Q ) , . . . , f ( s } ( x ) is equal to s+1 , the additional information given by the integral J f(t)dt increases the order by two.