Yazar "Shar, Muhammad Ali" seçeneğine göre listele

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    Computational aspects of an epidemic model involving stochastic partial differential equations
    (World Scientific Publ Co Pte Ltd, 2023) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akguel, Ali; Raza, Ali; Rafiq, Muhammad; Shar, Muhammad Ali
    This paper deals with the study of the reaction-diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.
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    Öğe
    Exact and solitary wave structure of the tumor cell proliferation with LQ model of three dimensional PDE by newly extended direct algebraic method
    (Aip Publishing, 2023) Ghazanfar, Sidra; Ahmed, Nauman; Ali, Syed Mansoor; Iqbal, Muhammad Sajid; Akgul, Ali; Shar, Muhammad Ali; Bariq, Abdul
    An essential stage in the spread of cancer is the entry of malignant cells into the bloodstream. The fundamental mechanism of cancer cell intravasation is still completely unclear, despite substantial advancements in observing tumor cell mobility in vivo. By creating therapeutic methods in conjunction with control engineering or by using the models for simulations and treatment process evaluation, tumor growth models have established themselves as a crucial instrument for producing an engineering backdrop for cancer therapy. Because tumor growth is a highly complex process, mathematical modeling has been essential for describing it because a carefully crafted tumor growth model constantly describes the measurements and the physiological processes of the tumors. This article discusses the exact and solitary wave behavior of a tumor cell with a three-dimensional linear-quadratic model. Exact solutions have been discussed in detail using the newly extended direct algebraic method, which presents a variety of answers to this issue based on the conditions applied. This article also illustrates its graphical behavior with surface and contour plots of several solitons.
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    Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by 06-modal expansion method
    (Elsevier, 2023) Shahzad, Tahir; Ahmad, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Ali, Syed Mansoor; Akguel, Ali; Shar, Muhammad Ali
    The current study deals with the exact solutions of nonlinear confirmable time fractional Sobolev type equations. Such equations have applications in thermodynamics, the flow of fluid through fractured rock. The underlying models are 2D equation of a semi-conductor with heating and Sobolev equation in 2D unbounded domain. These equation are used to describe the different aspects in semi-conductor. The analytical solutions of underlying models is not addressed yet or it is difficult to find. We gain the exact solutions of such models with help of analytical technique namely 06-model expansion method. The abundant families of solutions are obtained by the Jacobi elliptic function and it will give us soliton and solitary wave solutions. So, we extract the different types of solutions such as, dark, bright, singular, combine, periodic and mixed periodic. The unique physical problems are selected from a variety of the solutions that will help the reader for the verification and data experiment. The graphical behavior of the underlying models is represented in the form of 3D, line graphs and their corresponding contours for the various values of the parameters.