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Keywords = Daftardar-Gejji-Jafari decomposition technique

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26 pages, 378 KiB  
Article
Some New Quantum Numerical Techniques for Solving Nonlinear Equations
by Kamsing Nonlaopon, Awais Gul Khan, Farah Ameen, Muhammad Uzair Awan and Clemente Cesarano
Symmetry 2022, 14(9), 1829; https://doi.org/10.3390/sym14091829 - 3 Sep 2022
Cited by 4 | Viewed by 1661
Abstract
In this paper, we introduce some new quantum numerical techniques of midpoint and trapezoidal type essentially by using the decomposition technique. We also check the order of convergence of our suggested iterative methods. Numerical examples demonstrate that the new q-iterative methods can [...] Read more.
In this paper, we introduce some new quantum numerical techniques of midpoint and trapezoidal type essentially by using the decomposition technique. We also check the order of convergence of our suggested iterative methods. Numerical examples demonstrate that the new q-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. Full article
17 pages, 355 KiB  
Article
On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus
by Gul Sana, Pshtiwan Othman Mohammed, Dong Yun Shin, Muhmmad Aslam Noor and Mohammad Salem Oudat
Fractal Fract. 2021, 5(3), 60; https://doi.org/10.3390/fractalfract5030060 - 25 Jun 2021
Cited by 18 | Viewed by 3363
Abstract
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q [...] Read more.
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q-iterative methods by using the q-analogue of the Taylor’s series and the coupled system technique. In the domain of q-calculus, we determine the convergence of our proposed q-algorithms. Numerical examples demonstrate that the new q-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 q-Iterative methods. Full article
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