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ARTICLE

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 Duan^{4, 5}

1 Department of Mathematics, Saint Xavier University, Chicago, IL 60655-3105, U.S.A.
2 316 S. Maple St., Hartford, MI 49057-1225, U.S.A.
3 Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Faculty of Science, Department of Mathematics, Riyadh 11623, Saudi Arabia.
4 School of Sciences, Shanghai Institute of Technology, Fengxian District, Shanghai 201418, P.R. China.
5 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.

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Keywords

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