Wavelet-Galerkin Method and Some Numerical Method for Lane-Emden Type Differential Equation

Jafar Biazar^1, and Fereshteh Goldoust¹

¹Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Guilan, Rasht, Iran

Cite this paper

Jafar Biazar and Fereshteh Goldoust. Wavelet-Galerkin Method and Some Numerical Method for Lane-Emden Type Differential Equation. American Journal of Applied Mathematics and Statistics. 2013; 1(5):83-86. doi: 10.12691/AJAMS-1-5-1

Abstract

In this paper, we will compare the performance of Adomian decomposition method and the wavelet-Galerkin method applied to the Lane-Emden type differential equation. The Galerkin Wavelet method (GWM), which is known as a numerical approach is used for the Lane- Emden equation, as an initial value problem. This approach consists of using integral operator, to convert the Lane- Emden equation in to an integral equation, then applying Galerkin Wavelet method to solve the resulted integral equation. The properties of Galerkin Wavelet method (GWM) and the Adomian Decomposition Method are also addressed. Although the Adomian decomposition solution required slightly more computational effort than the wavelet-Galerkin solution, it resulted in more accurate results than the wavelet-Galerkin method. To illustrate the methods two examples are provided and the results are in good agreement with exact solution.

Keywords

Galerkin Wavelet, Adomian Decomposition method, Lane-Emden equation, integral equations

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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