On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

• Main Authors: Gul Sana, Pshtiwan Othman Mohammed, Dong Yun Shin, Muhmmad Aslam Noor, Mohammad Salem Oudat
• Format: Article
• Language: English
• Published: MDPI AG 2021-06-01
• Series: Fractal and Fractional
• Subjects: Taylor’s series in <i>q</i>-calculus; iterative methods; convergence analysis; Daftardar-Gejji–Jafari decomposition technique
• Online Access: https://www.mdpi.com/2504-3110/5/3/60

Quantum calculus (also known as the <i>q</i>-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving <i>q</i>-analogous results without the use of the limits. In this paper, we suggest and analyze some new <i>q</i>-iterative methods by using the <i>q</i>-analogue of the Taylor’s series and the coupled system technique. In the domain of <i>q</i>-calculus, we determine the convergence of our proposed <i>q</i>-algorithms. Numerical examples demonstrate that the new <i>q</i>-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. These newly established methods also exhibit predictability. Furthermore, an analogy is settled between the well known classical methods and our proposed <i>q</i>-Iterative methods.