Yazar "Shahid, Naveed" seçeneğine göre listele

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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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    Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Akgul, Ali; Rehman, Muhammad Aziz ur; Ahmed, Nauman; Iqbal, Muhammad Sajid; Shahid, Naveed; Rafiq, Muhammad
    In this article, the transmission dynamical model of the deadly infectious disease namedEbola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan(now South Sudan) and was identified in 1976. The novelty of the model under discussion is theinclusion of advection and diffusion in each compartmental equation. The addition of these two termsmakes the model more general. Similar to a simple population dynamic system, the prescribed modelalso has two equilibrium points and an important threshold, known as the basic reproductive number.The current work comprises the existence and uniqueness of the solution, the numerical analysis ofthe model, and finally, the graphical simulations. In the section on the existence and uniqueness ofthe solutions, the optimal existence is assessed in a closed and convex subset of function space. Forthe numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate thesolution of the continuous mathematical model. The main reason for the adoption of this technique isdelineated in the form of the positivity of the state variables, which is necessary for any populationmodel. The positivity of the applied scheme is verified by the concept of M-matrices. Since thenumerical method gives a discrete system of difference equations corresponding to a continuoussystem, some other relevant properties are also needed to describe it. In this respect, the consistencyand stability of the designed technique are corroborated by using Taylor's series expansion and Von Neumann's stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.
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    Dynamical study of groundwater systems using the new auxiliary equation method
    (Elsevier, 2024) Shahid, Naveed; Baber, Muhammad Zafarullah; Shaikh, Tahira Sumbal; Iqbal, Gulshan; Ahmed, Nauman; Akgul, Ali; De la Sen, Manuel
    In this research, the exact solitary wave solutions to the non-linear problem of underground water levels are found. This study examines the transport of solutes in groundwater systems with variable density flow. The mathematical equation that is used to explain how groundwater moves through an aquifer is known as the groundwater flow equation and is used in hydrogeology. The auxiliary equation method is used to gain the analytical solutions to the underlying model equation. These solutions are gained in the form of hyperbolic, trigonometric, exponential, and rational function solutions. Mathematica generates two-dimensional and threedimensional graphs with suitable parameter values. The resulting solutions are also useful for researching wave interactions in several novel structures.
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    Öğe
    On the Soliton Solutions for the Stochastic Konno-Oono System in Magnetic Field with the Presence of Noise
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Baber, Muhammad Zafarullah; Ahmed, Nauman; Shahid, Naveed; Akgul, Ali; de la Sen, Manuel
    In this study, we consider the stochastic Konno-Oono system to investigate the soliton solutions under the multiplicative sense. The multiplicative noise is considered firstly in the Stratonovich sense and secondly in the Ito sense. Applications of the Konno-Oono system include current-fed strings interacting with an external magnetic field. The F-expansion method is used to find the different types of soliton solutions in the form of dark, singular, complex dark, combo, solitary, periodic, mixed periodic, and rational functions. These solutions are applicable in the magnetic field when we study it at the micro level. Additionally, the absolute, real, and imaginary physical representations in three dimensions and the corresponding contour plots of some solutions are drawn in the sense of noise by the different choices of parameters.