Abstract:

 We first presented a  family of three\|parameter third\|order convergence iteration method for solving nonlinear equations and obtained different iteration methods by taking different values of the parameters.  We then proveed that the iteration methods have third-order convergence similar to those of existing methods, our methods also avoid computing the second derivative. Finally, we tested the methods on several numerical examples and illustrated that our methods are competitive with several other methods.

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