Approximate Solution of Emden-Fowler Equation Using the Galerkin Method

Aswhad, Asmaa A.

doi:10.37652/juaps.2023.178798

	Approximate Solution of Emden-Fowler Equation Using the Galerkin Method
Journal of University of Anbar for Pure Science
Volume 17, Issue 1, June 2023, Pages 200-203 PDF (688.08 K)
Document Type: Research Paper
DOI: 10.37652/juaps.2023.178798
Author
Asmaa A. Aswhad^*
Department of Mathematics, College of Education for pure Science Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq;
Abstract
The Emden-Fowler equation (E-F.Eq.) used in mathematical with other science like physics, chemical physics and astrophysics, also this equation can be reduces to the Lane–Emden equation with specified function and used it in different sciences with mathematics. Many Authors study analytic and numerical methods to find the solution for this kind of the equations in the case linear or nonlinear one of these methods the homotopy-perturbation method. In this work the approximate solution for generalized (E-F.Eq.) in the second order ordinary differential equations was found by Galerkin method which is one of the weighted residual methods and do not need long time also use operator (linear or nonlinear) or differential operator in the any kind of the intervals and compared this solution with the exact solution by discuss the results from applying this method for homogeneous and nonhomogeneous equations and drown the solutions in the same figure to illustrate the results.
Keywords
Emden-Fowler Equation; weighted residual method; Galerkin method
Supplementary Files 19 Math.doi.pdf
References
A. Aswhad and S. M. Yassein, Sumudu Iterative Method for Solving Nonlinear Partial Differential Equations, Ibn Al-Haitham Jour. for Pure & Appl. Sci.,Vol. 34(2), pp. 23-32, 2021. S. Mohammed, Iterative Method for Solving a Nonlinear Fourth Order Integro-Differential Equation, Ibn Al-Haitham Jour. for Pure & Appl. Sci.,Vol. 35(3), pp. 206–212, 2022. S.H. Chowdhury and I. Hashim, Solutions of Emden–Fowler equations by homotopy-perturbation method, Nonlinear Analysis: Real World Applications, Vol.10, pp.104–115, 2009. J. Mohammed and M. A. Mohammed, Runge- Kutta Numerical Method for Solving Nonlinear Influenza Model, Ibn Al-Haitham Int. Con. for Pure and App.Sciences (IHICPS), Jou. of Phy. Con. Series 1879(2021)032040,doi:10.1088/1742-6596/1879/3/032040. A. Al-Hawasy, The Approximation Solution of a Nonlinear Boundary Value Problem Via Galerkin Finite Elements Method with Crank-Nicolson, Ibn Al-Haitham Jour. for Pure & Appl. Sci., Vol. 31(3), pp. 126-134, 2018. H. Abd Almjeed, Compare Between Least Square Method and Petrov-Galerkin Method for Solving the First Order Linear Ordinary Delay Differential Equations, Journal of College of Education for pure sciences(JCEPS), Vol. 7, Number 4, pp. 16-27, December 2017. U. Richardson, The Emission of Electricity from Hot Bodies, London, 1921. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover, New York, 1967. N. Reddy, An introduction to the finite element Method, Third Edition, McGraw-Hill Series in Mechanical Engineering, Copyright © 2006. B Bochev,. and M.D. Gunzburger, Finite Element Methods of Least-Square Type, SIAM Review, Vol.40, pp.789-837, 1998. A. Aswhad, Approximate Solution of Delay Differential Equations Using the Collocation Method Based on Bernstien Polynomials, Baghdad Science Journal, Vol.8(3), pp.820-825, 2011. I. Ramos, Linearization techniques for singular initial-value problems of ordinary differential equations, Appl. Math. Com., Vol.161, pp.525–542, 2005. A.M. Wazwaz, Adomian decomposition method for a reliable treatment of the Emden–Fowler equation, Appl. Math. Comput. Vol. 161, pp. 543–560, 2005.
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