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Ebrahimzadeh, Asiyeh, Keshavarz Hedayati, Elham. (1405). An efficient numerical solution of the optimal control mathematical models for pollutant spread through forest resources based on shifted Bernoulli polynomials. سامانه مدیریت نشریات علمی, 14(1), 305-315. doi: 10.22034/cmde.2025.63589.2838
Asiyeh Ebrahimzadeh; Elham Keshavarz Hedayati. "An efficient numerical solution of the optimal control mathematical models for pollutant spread through forest resources based on shifted Bernoulli polynomials". سامانه مدیریت نشریات علمی, 14, 1, 1405, 305-315. doi: 10.22034/cmde.2025.63589.2838
Ebrahimzadeh, Asiyeh, Keshavarz Hedayati, Elham. (1405). 'An efficient numerical solution of the optimal control mathematical models for pollutant spread through forest resources based on shifted Bernoulli polynomials', سامانه مدیریت نشریات علمی, 14(1), pp. 305-315. doi: 10.22034/cmde.2025.63589.2838
Ebrahimzadeh, Asiyeh, Keshavarz Hedayati, Elham. An efficient numerical solution of the optimal control mathematical models for pollutant spread through forest resources based on shifted Bernoulli polynomials. سامانه مدیریت نشریات علمی, 1405; 14(1): 305-315. doi: 10.22034/cmde.2025.63589.2838

An efficient numerical solution of the optimal control mathematical models for pollutant spread through forest resources based on shifted Bernoulli polynomials

Computational Methods for Differential Equations
مقاله 21، دوره 14، شماره 1، فروردین 2026، صفحه 305-315    اصل مقاله (589.28 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63589.2838
نویسندگان
Asiyeh Ebrahimzadeh؛ Elham Keshavarz Hedayati*
Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.
چکیده
This study presents a computational method for solving a mathematical model of optimal control for pollutant spread through forest resources using shifted Bernoulli polynomials (SBPs). The model is formulated as an optimal control problem governed by a system of ordinary differential equations, which is then transformed into a nonlinear programming problem (NLP) using the collocation approach and operational matrix of derivatives based on SBPs. The NLP is employed to obtain numerical solutions, and the results demonstrate the proposed method’s acceptability for modeling pollutant spread through forest resources. The study advises three controls on both types of industries (wood-based and non-wood-based) and forest resources to reduce pollution.
کلیدواژه‌ها
Pollutants؛ Optimal control؛ Forest resources؛ Shifted Bernoulli polynomials؛ Collocation method
مراجع
  • [1] E. Buhe, M. Rafiullah, D. Jabeen, and N. Anjum, Application of homotopy perturbation method to solve a nonlinear mathematical model of depletion of forest resources, Frontiers in Physics, 11 (2023), 1246884.
  • [2] A. Eswari, S. V. Raj, and V. S. Priya, Analysis of mathematical modeling the depletion of forestry resource: effects of population and industrialization, Matrix Sci. Math., 3(2) (2019), 22–26.
  • [3] G. Freud, Orthogonal polynomials, Pergamon Press, 1971.
  • [4] Q. Gong, I. M. Ross, W. Kang, and F. Fahroo, On the pseudospectral covector mapping theorem for nonlinear optimal control, in Proceedings of the 45th IEEE conference on decision and control, IEEE, (2006), 2679–2686.
  • [5] M. D. Goshu and M. F. Endalew, Mathematical modeling on conservation of depleted forestry resources, Nat. Resour. Model., 35(2) (2022), e12338.
  • [6] E. Keshavarz, Y. Ordokhani, and M. Razzaghi, A numerical solution for fractional optimal control problems via Bernoulli polynomials, J. Vib. Control, 22(18) (2016), 3889–3903.
  • [7] E. Keshavarz, Y. Ordokhani, and M. Razzaghi, Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Model., 38(24) (2014), 6038– 6051.
  • [8] R. Khanduzi, A. Ebrahimzadeh, and Z. Ebrahimzadeh, A combined Bernoulli collocation method and imperialist competitive algorithm for optimal control of sediment in the dam reservoirs, AUT J. Math. Comput., 5(1) (2024), 71–80.
  • [9] E. Kreyszig, Introductory Functional Analysis With Applications, New York, John Wiley, 1978.
  • [10] D. G. Luenberger and Y. Ye, Linear and nonlinear programming, Springer, New York, 2008.
  • [11] K. Maleknejad and A. Ebrahimzadeh, An efficient hybrid pseudo-spectral method for solving optimal control of Volterra integral systems, Math. Commun. 19 (2014), 417–435.
  • [12] A. K. Misra and K. Lata, Depletion and conservation of forestry resources: a mathematical model, Diff. Equ. Dyn. Syst., 23 (2015), 25–41.
  • [13] C. Mohan, Solution of real life optimization problems, in Statistical modeling and applications on real-time problems, CRC Press, 2024, 152–170.
  • [14] S. Nemati and D. F. Torres, Application of bernoulli polynomials for solving variable-order fractional optimal control-affine problems, Axioms, 9(4) (2020), 114.
  • [15] R. Pathak, Depletion of forest resources and wildlife population with habitat complexity: A mathematical model, Open J. of Ecol., 8(11) (2018), 579.
  • [16] S. Qureshi and A. Yusuf, Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator, Chaos Solitons Fractals, 126 (2019), 32–40.
  • [17] N. H. Shah, M. H. Satia, and B. M. Yeolekar, Optimum control for spread of pollutants through forest resources, Appl. Math., 8(5) (2017), 607–620.
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