Novel Parametric Families of with and without Memory Iterative Methods for Multiple Roots of Nonlinear Equations

The methods that use memory using accelerating parameters for computing multiple roots are almost non-existent in the literature. Furthermore, only paper available this direction showed an increase order of convergence 0.5 from without to with extension. In paper, we introduce a new fifth-order method, which subsequently extend two higher-order self-accelerating parameter. proposed extension demonstrate significant improvement 5 7, making first achieve at least 2-order improvement. addition improvement, our is also Hermite interpolating polynomials approximate parameter roots. We provide rigorous theoretical proofs theorems establish methods. Finally, potential impact through numerical experimentation on diverse range problems. Overall, believe have various applications science and engineering.