Open AccessApplication of Analytic Approximation Method Using HAM for Solving The Democratic Elections Model
Author(s) -
Benny Yong
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1320/1/012024
Subject(s) - power series , population , mathematics , population model , homotopy analysis method , series (stratigraphy) , simple (philosophy) , power (physics) , differential equation , mathematical optimization , homotopy , mathematical analysis , pure mathematics , physics , paleontology , philosophy , demography , epistemology , quantum mechanics , sociology , biology
This article presents the solutions of the democratic elections model by homotopy analysis method (HAM). We proposed a simple democratic elections model in the form non-linear differential equation in a closed voters population. Voters population divided into three sub-population, i.e neutral sub-population, supportive sub-population, and aphatetic sub-population. HAM is applied to compute the solutions of the model. HAM is an analytic approximation method in the form of power series to solve the non-linear differential equation. HAM contains the auxiliary parameter for controlling the convergent region of power series solutions. Numerical simulations on the model in the form graphical results are presented and discussed quantitatively to describe the dynamics of each sub-population. It is shown that HAM performs well in terms of efficiency which converge rapidly and results obtained require only a few iterations.