Yazar "Saqib, Muhammad" seçeneğine göre listele

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    An efficient numerical method for solving m-polar fuzzy initial value problems
    (Springer Science and Business Media Deutschland GmbH, 2022) Akram, Muhammad; Saqib, Muhammad; Bashir, Shahida; Allahviranloo, Tofigh
    Several problems in the field of science and technology are modeled with information about the situation that is ambiguous, imprecise, or incomplete. That is, the information about values of parameters, functional relationships, or initial conditions is not given in precise. In these circumstance, existing analytic or numerical methods can be applied only to the selected behavior of the system. For example, by fixing the values of unknown parameters to some credible values. On the basis of partial knowledge, it is impossible to describe the behavior of complete system. Thus, fuzzy differential equations arise in many dynamical models. In modeling of several real-world problems, differential equations frequently involve multi-agent, multi-index, multi-objective, multi-attribute, multi-polar information or uncertainty rather than a single bit. These type of differential equations cannot be well represented by means of fuzzy differential equations or bipolar fuzzy differential equations. Therefore, the theory of m-polar fuzzy sets can be applied to differential equations to handle the problems which have multi-polar information. The aim of this paper is to study differential equation in m-polar fuzzy environment. A fourth-order Runge–Kutta method to solve m-polar FIVPs is presented. The consistency, stability and convergence of suggested method are discussed to ensure its efficiency and validity. Since it requires no higher order function derivatives, the suggested method is straightforward to implement. Euler and Euler modified methods have global truncations errors of O(h) and O(h2) respectively whereas the suggested Runge–Kutta’s global truncation errors of O(h4). Numerical examples are provided to compare the proposed method with Euler and modified Euler methods in terms of global truncation errors (GTE). The numerical findings suggest that the purposed method has an adequate level of accuracy. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
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    Fourth- and fifth-order iterative schemes for nonlinear equations in coupled systems: A novel Adomian decomposition approach
    (Elsevier, 2023) Saqib, Muhammad; Ahmad, Daud; Al-Kenani, Ahmad N.; Allahviranloo, Tofigh
    In the fields of numerical analysis and applied science, approximating the roots of nonlinear equations is a fundamental and intriguing challenge. With the rapid advancement of computing power, solving nonlinear equations using numerical techniques has become increasingly important.Numerical methods for nonlinear equations play a critical role in many areas of research and industry, enabling scientists and engineers to model and understand complex systems and make accurate predictions about their behavior. This paper aims to propose novel fourth- and fifth-order iterative schemes for approximating solutions to nonlinear equations in coupled systems using Adomian decomposition methods. The proposed method's convergence is examined and numerical examples are provided to demonstrate the effectiveness of the new schemes. We compare these iterative techniques with some previous schemes in the literature, and our results show that the new schemes are more efficient. Our findings represent a significant improvement over previously reported results. Polynomiography is an important tool for visualizing the roots of complex polynomials. It is widely used by researchers, mathematicians and engineers, as it provides a way to visualize complex equations understand their behavior. Our proposed method is capable of generating polynomiographs of complex polynomials, revealing interesting patterns that provide clear visual representations of the roots of complex polynomials. (C) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).