A Numerical Solution of Mathematical Models for Pollutant Spread through Forest Resources Using Bernoulli Polynomials

چکیده مقاله

ABSTRACT: This study propounds 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 applying the collocation approach based on shifted OBPs. Newton’s method is employed to derive numerical solutions, and the results are compared with those obtained by using the Runge–Kutta method of fourth order (RK4) to demonstrate the efficiency of the proposed method. The results show good agreement with the RK4 method, indicating our method’s acceptability for modeling spreading of pollutants through forest resources. © Pleiades Publishing, Ltd. 2026.