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k. Abbaoui, Y. Cherruault, Convergence of Adomian’s method applied to differential equations, Comput. Math. Appl. 28 (1994) 103-109.

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Article

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

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


American Journal of Applied Mathematics and Statistics. 2013, Vol. 1 No. 5, 83-86
DOI: 10.12691/ajams-1-5-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Jafar Biazar, 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.

Correspondence to: Jafar Biazar, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Guilan, Rasht, Iran. Email: biazar@guilan.ac.ir

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.

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