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.
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Ebrahimzadeh, A. and Keshavarz Hedayati, E. (2026). 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, 14(1), 305-315. doi: 10.22034/cmde.2025.63589.2838
MLA
Ebrahimzadeh, A. , and Keshavarz Hedayati, E. . "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, 14, 1, 2026, 305-315. doi: 10.22034/cmde.2025.63589.2838
HARVARD
Ebrahimzadeh, A., Keshavarz Hedayati, E. (2026). '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, 14(1), pp. 305-315. doi: 10.22034/cmde.2025.63589.2838
CHICAGO
A. Ebrahimzadeh and E. Keshavarz Hedayati, "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, 14 1 (2026): 305-315, doi: 10.22034/cmde.2025.63589.2838
VANCOUVER
Ebrahimzadeh, A., Keshavarz Hedayati, E. 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, 2026; 14(1): 305-315. doi: 10.22034/cmde.2025.63589.2838
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