Computing multiple zeros by using a parameter in Newton-Secant method
This is an incremental improvement for numerical analysts working on root-finding algorithms.
The paper modifies the Newton-Secant method to achieve third-order convergence for finding multiple roots of nonlinear equations, requiring two function evaluations and one derivative evaluation per iteration, with an efficiency index of approximately 1.442. Numerical experiments and dynamical analysis demonstrate its performance compared to existing methods.
In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first derivative. This method has the efficiency index equal to $3^{\frac{1}{3}}\approx 1.44225$. We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the dynamics of the proposed method are shown with some comparisons to the other existing methods.