The Application of Homotopy Perturbation Method to Solve Nutrition Recycle Problems

Abstract

Ecosystem is an ecological system that is formed by a mutual inseparable relationship between living organism and environment. The interaction among the components within an ecosystem, especially the nutrition recycle, can be modeled by using mathematical equation. The nutrition recycle model can be classified as a nonlinear problem. This phenomenon can be best represented by homotopy perturbation method. Homotopy perturbation method is defined as an analytical approach to solve a nonlinear problem. Based on this method, it can be concluded that the solution of nutrition recycle problem has a form of power series. By using MATHEMATICA software, it has been shown that the higher order of series used, the better model can be obtained. The model is expected to resemble the real solution. If the growth rate of autotroph is higher than its mortality rate, then the amount of abiotic nutrition and detritus organism will be declining, but the number of autotroph will increase. In the case rate of equal growth and mortality rate of autotroph, it will result into a decrease in abiotic nutrition, detritus organism, and autotroph number.