Browsing by Author "Shahid, Naveed"

Now showing 1 - 2 of 2

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, Naveed...et al. (2021). "Numerical investigation for the nonlinear model of hepatitis-B virus with the existence of optimal solution". AIMS MATHEMATICS. Vol: 6, No: 8, pp. 8294-8314.
Numerical investigation for the nonlinear model of hepatitis-B virus with the existence of optimal solution
(2021) Shahid, Naveed; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; 56389
In the recent article, a reaction-advection-diffusion model of the hepatitis-B virus (HBV) is studied. Existence and uniqueness of the optimal solution for the proposed model in function spaces is analyzed. The advection and diffusion terms make the model more generic than the simple model. So, the numerical investigation plays a vital role to understand the behavior of the solutions. To find the existence and uniqueness of the optimal solutions, a closed and convex subset (closed ball) of the Banach space is considered. The explicit estimates regarding the solution of the system for the admissible auxiliary data is computed. On the other hand, for the numerical approximation of the solution, an elegant numerical technique is devised to find the approximate solutions. After constructing the discrete model, some fundamental properties must necessarily be possessed by the proposed numerical scheme. For instance, consistency, stability, and positivity of the solutions. These properties are carefully studied in the current article. To prove the positivity of the proposed scheme, M-matrix theory is used. All the above mentioned properties are verified by sketching the graph via simulations. Furthermore, these plots are helpful to understand the true behavior of the solutions. For this purpose, a fruitful discussion is included about the simulations to justify our results.