New modification of Maheshwari method with optimal eighth order of convergence for solving nonlinear equations
This is an incremental improvement for researchers working on iterative methods for nonlinear equations.
The paper presents a family of three-point eighth-order convergence methods for solving nonlinear equations, achieving an efficiency index of 1.682 with three function evaluations and one derivative evaluation per iteration.
In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. This class of methods has the efficiency index equal to $8^{\frac{1}{4}}\approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods.