Dynamics and applications of quantum iterative methods

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 آذر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.95542.1738

نویسندگان

Sapan Kumar Nayak¹؛ P. K. Parida^{* 2}؛ Babita Mehta²

¹Department of Mathematics, Usha Martin University, Ranchi-835103, India.

²Department of Mathematics, Central University of Jharkhand, Ranchi-835222, India.

چکیده

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.

کلیدواژه‌ها

Nonlinear equations؛ $q$-derivative؛ Basin of attraction؛ Scaling theorem؛ Dynamical plane