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Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method

Abdul-Majid Wazwaz1, R,olph Rach2, Lazhar Bougoffa3, Jun-Sheng Duan4, 5
Department of Mathematics, Saint Xavier University, Chicago, IL 60655-3105, U.S.A.
316 S. Maple St., Hartford, MI 49057-1225, U.S.A.
Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Faculty of Science, Department of Mathematics, Riyadh 11623, Saudi Arabia.
School of Sciences, Shanghai Institute of Technology, Fengxian District, Shanghai 201418, P.R. China.
Corresponding author. Email: duanjs@sit.edu.cn; duanjssdu@sina.com

Computer Modeling in Engineering & Sciences 2014, 100(6), 507-529. https://doi.org/10.3970/cmes.2014.100.507

Abstract

In this paper, we construct the Lane–Emden–Fowler type equations of higher orders. We study the linear and the nonlinear Lane–Emden–Fowler type equations of the third and fourth orders, where other forms can be treated in a similar manner. We use the systematic Adomian decomposition method to handle these types of equations with specified initial conditions. We confirm that the Adomian decomposition method provides an efficient algorithm for exact and approximate analytic solutions of these equations. We corroborate this study by investigating several numerical examples that emphasize initial value problems.

Keywords

Initial value problems, Singularities, Lane–Emden–Fowler equation, Adomian decomposition method, Adomian polynomials

Cite This Article

Wazwaz, A., Rach, R., Bougoffa, L., Duan, J. (2014). Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method. CMES-Computer Modeling in Engineering & Sciences, 100(6), 507–529.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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