Application of homotopy perturbation method to solve a nonlinear mathematical model of depletion of forest resources

Abstract

Reduction in forest resources due to increasing global warming and population growth is a critical situation the World faces today. As these reserves decrease, it alarms new challenges that require urgent attention. In this paper, we provide a semi-analytical solution to a nonlinear mathematical model that studies the depletion of forest resources due to population growth and its pressure. With the help of the homotopy perturbation method (HPM), we determine an approximate series solution with few perturbation terms, which is one of the essential power of the HPM method. We compare our semi-analytical results with numerical solutions obtained using the Runge-Kutta 4th-order (RK-4) method. Furthermore, we analyze the model’s behaviour and dynamics by changing the parametric coefficients that represent the depletion rate of forest resources and the growth rate of population pressure and present these findings using various graphs.