Computing multiple zeros by using a parameter in Newton-Secant method

In this paper, we modify the Newton–Secant method with third order of convergence for finding multiple roots of nonlinear equations. This method requires two evaluations of the function and one evaluation of its first derivative per iteration. This method has the efficiency index equal to 313≈1.44225 3 1 3 ≈ 1.44225 . We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the attraction basins of the proposed method are shown and compared with other existing methods.