... 2025 09 09 2025 01 10 2025 © Emerald Publishing Limited 2025 Emerald Publishing Limited Licensed re-use rights only Nonlinear equations Method with-memory Order of convergence Efficiency index Complex dynamics 65H05 41A25 65D05 Finding the solution...

...Dongdong Ruan; Xiaofeng Wang; Yan Wang Purpose The purpose of this paper is to study local convergence and applications of a new seventh-order iterative method. Design/methodology/approach The order of convergence for the method is proved by using Taylor expansions. In addition, local...

... Limited Licensed re-use rights only Iterative method Polar decomposition Matrix sign function Polar factor Order of convergence Yang-Baxter-like equation 15A24 65F10 65F30 In recent years, much attention has been given in the literature to solve matrix equations (Erfanifar...

... Quasilinearization Differential quadrature method Runge‐Kutta method Order of convergence Differential equations Mathematics Consider the one‐dimensional non linear partial equation: Equation 1 with the initial condition: Equation 2 and the boundary conditions: Equation 3 where v...

... in physics and engineering. The purpose of this paper is to propose two new modified Newton's method for solving non‐linear equations. Convergence results show that the order of convergence of the proposed iterative methods for a simple root is four. The iterative methods are free from second derivative...