VIM and FDM for solving boltzmann equation of self-gravitating gas-dust system

Abstract

In this research, Boltzmann equation of Self-Gravitating Gas-Dust System is introduced. The model consists of dust component equations, gas dynamics equations and also Poisson equation. The mathematical model is used in order to visualize the movement of the gas and dust in environment. This research only focuses on sequential algorithm and solving the model in 2 Dimension (2-D). Numerical solutions obtained by using the Variational Iteration Method (VIM) and Finite Difference Method (FDM). The results are computed by using Borland C++ Builder, MATLAB 2008a and MAPLE 13. Then, the graphs are visualized by using Microsoft excel. The result is based on numerical analysis. Numerical analysis under consideration is pattern of the graph, gradient of the graph, time execution and computational complexity. The movement of the gas-dust showed differently with the different method. At the end, the results show that the VIM and FDM are successfully in visualizing the movement of the gas-dust in reality. Based on theoretically, VIM is in solving gas-dust problem compared to FDM.