Pollution dynamics in an interconnected lake system: modeling and simulation using the finite element method

• Autorzy: Adel Mohamed , Khader Mohamed M.

Identyfikatory

DOI

10.17512/jamcm.2025.1.01

• Języki publikacji: EN

Abstrakty

EN

In this research, we present a real-world simulation to evaluate the pollution dynamics within a network of three interconnected lakes, facilitated by canals. Using the finite element method (FEM), we handle three input models: linear, periodic, and exponentially decaying. This procedure turns the specified model into an algebraic equations system. By analyzing the residual error function (REF), we can verify the offered technique’s accuracy and efficiency. The numerical outputs are contrasted with that of the fourth-order Runge-Kutta (RK4M). Our results confirm that the presented algorithm is a practical tool to simulate the solution of such models. Key advantages of the supposed approach include simplicity, absence of secular components, and independence from perturbation parameters.

Słowa kluczowe

EN

pollution model for the lakes system; finite element method; RK4M; REF

PL

model zanieczyszczenia dla systemu jezior; metoda elementów skończonych; RK4M; REF

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 1
• Strony: 5--17
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Adel Mohamed

• Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA

autor

Khader Mohamed M.

• Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA
• Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Bibliografia

• [1] Biazar, J., Shahbala, M., & Ebrahimi, H. (2010). VIM for solving the pollution problem of a system of lakes. Journal of Control Science and Engineering, 10, 1-6.
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• [7] Khader, M.M., & Adel, M. (2020). Numerical approach for solving the Riccati and logistic equations via QLM-rational Legendre collocation method. Comput. Appl. Math., 39, 1-9.
• [8] Adel, M., Sweilam, N.H., & Khader, M.M. (2024). On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM. Journal of Applied Mathematics and Computational Mechanics, 23(1), 7-18.
• [9] Khan, U., Zaib, A., Ishak, A., & Bakar, S.A. (2021). Time-dependent Blasius-Rayleigh-Stokes f lowconveying hybrid nanofluid and heat transfer induced by non-Fourier heat flux and transitive magnetic field. Case Studies in Thermal Engineering, 26, 1-13.
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• [21] Adel, M., Sweilam, N.H., & Khader, M.M. (2023). Semi-analytical scheme with its stability analysis for solving the fractional-order predator-prey equations by using Laplace-VIM. Journal of Applied Mathematics and Computational Mechanics, 22(4), 5-17.
• [22] Adel, M., & Khader, M.M. (2023). Theoretical and numerical treatment for the fractal-fractional model of pollution for a system of lakes using an efficient numerical technique. Alexandria Engineering Journal, 82(1), 415-425.
• [23] Benhammouda, B., Leal, H.V., & Martinez, L.H. (2014). Modified DTM for solving the model of pollution for a system of lakes. Discrete Dynamics in Nature and Society, 2014, 1-12.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).