Abstract:

We presented a family of iteration methods for solving the approximate solutions of the nonlinear equations f(x)=0. We
 proved the iteration methods have third\|order convergence, and the methods have the advantage of avoiding the computation of the second Frechet derivative. We performed different numerical tests that confirm the theoretical results. Our methods can compete with Newton’s method and some cl
assical thirdorder methods.

Key words: nonlinear equation, iteration methods, convergence of order, Newton’s method