Dynamics and applications of quantum iterative methods

In this article, we have introduced a new type of parametric family of the Quantum iterative method (PFQIM) using quantum derivative (q-derivative) to solve non-linear equations. The stability and convergence analysis of the proposed family of methods are shown to be studied using dynamic graphs. The dynamical and convergence planes of methods are studied using complex and real dynamics, respectively. In complex dynamics, we have provided the scaling theorem for PFQIM in order to study affine conjugacy classes of iterative methods. Moreover, the influence of the q-derivative and parameter of the method and how they affect the stability and convergence of the method are well discussed using real dynamics with some real-world applications.