Yazar "Rehman, Muhammad Aziz-ur" seçeneğine göre listele

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    A finite difference scheme to solve a fractional order epidemic model of computer virus
    (Amer Inst Mathematical Sciences-Aims, 2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Rafiq, Muhammad
    In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
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    A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Akgul, Ali; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Iqbal, Muhammad Sajid; Shahid, Naveed; Rafiq, Muhammad
    In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model.
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    New applications related to Covid-19
    (Elsevier, 2021) Akgul, Ali; Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur
    Analysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.
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    Structure Preserving Numerical Analysis of Reaction-Diffusion Models
    (Hindawi Ltd, 2022) Ahmed, Nauman; Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgul, Ali
    In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.