Browsing by Author "Shaikh, Tahira Sumbal"

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Citation Count: Shahid, Naveed...et al. (2020). "Novel numerical analysis for nonlinear advection-reaction-diffusion systems", Open Physics, Vol. 18, No. 1, pp. 112-125.
Novel numerical analysis for nonlinear advection-reaction-diffusion systems
(2020) Shahid, Naveed; Ahmed, Nauman; Baleanu, Dumitru; Alshomrani, Ali Saleh; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-u; Shaikh, Tahira Sumbal; Malik, Muhammad Rafiq; 56389
In this article, a numerical model for a Brusselator advection-reaction-diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.
Citation Count: Shahid, Naveeda...et al. (2021). "Optimality of solution with numerical investigation for coronavirus epidemic model", Computers, Materials and Continua, Vol. 67, no. 2, pp. 1713-1728.
Optimality of solution with numerical investigation for coronavirus epidemic model
(2021) Shahid, Naveeda; Baleanu, Dumitru; Ahmed, Nauman; Shaikh, Tahira Sumbal; Raza, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Aziz-Ur Rehman, Muhammad; 56389
The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-Temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated. Also, the solution to the considered system is made possible in a well-known functions space. For this purpose, a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space. The essential explicit estimates for the solutions are investigated for the associated auxiliary data. The numerical solution and its analysis are the crux of this study.Moreover, the consistency, stability, and positivity are the indispensable and core properties of the compartmentalmodels that a numerical designmust possess. To this end, a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system. The M-matrix theory is applied to prove the positivity of the design. The results for the consistency and stability of the design are also presented in this study. The plausibility of the projected scheme is indicated by an appropriate example. Computer simulations are also exhibited to conclude the results. © 2021 Tech Science Press. All rights reserved.