A numerical solution of the mathematical models for pollutant spread through forest resources by Bernoulli polynomials
Elham Keshavarz, Asiyeh Ebrahimzadeh
Department of Mathematics Education, Farhangian University, Tehran, Iran
Keywords: pollutants, forest resources, system of non-linear ordinary differential equations, shifted orthonormal Bernoulli polynomials, collocation method, numerical solution
Abstract
This study propounded a numerical approach for solving a mathematical model of pollutant spread through forest resources using shifted orthogonal Bernoulli polynomials (OBPs). The model is based on a system of ordinary differential equations, which is transformed into an algebraic system using the collocation approach based on shifted OBPs. Newton's method is employed to obtain numerical solutions, and the results are compared with those obtained using the Runge-Kutta method of fourth-order (RK4) to demonstrate the efficiency of the proposed method. The results demonstrate good agreement with the RK4 method, indicating the proposed method's acceptability for modeling pollutant spread through forest resources.
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