A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method
Open Access
- 8 July 2013
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2013, 1-10
- https://doi.org/10.1155/2013/378593
Abstract
A new analytic method is applied to singular initial-value Lane-Emden-type problems, and the effectiveness and performance of the method is studied. The proposed method obtains a Taylor expansion of the solution, and when the solution is polynomial, our method reproduces the exact solution. It is observed that the method is easy to implement, valuable for handling singular phenomena, yields excellent results at a minimum computational cost, and requires less time. Computational results of several test problems are presented to demonstrate the viability and practical usefulness of the method. The results reveal that the method is very effective, straightforward, and simple.Keywords
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