A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method

Abstract

In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c 1 , on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c 2 , on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.