A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

By Omar Abu Arqub, Ahmad El-Ajou, A. Sami Bataineh, Ishak Hashim. 2013

153 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/d8b0110b175365dcb183d367f17b681b95200c1f

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Citations in the corpus

A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method (2015, unknown): “Besides, the RPSM has been successfully applied to get numerical solutions for many other problems, for instance, generalized Lane-Emden equation which is a highly nonlinear singular differential equation [28], regular initial value problems [29], composite and noncomposite fractional differential e”
An Optimization Algorithm for Solving Systems of Singular Boundary Value Problems (2014, background): “On the other hand, the numerical solvability of other version of differential equations and other related equations can be found in [34,35,36,37,38, 39,40] and references therein.”
Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method (2015, methodology): “It has been successfully applied to handle the numerical solution of the generalized Lane-Emden equation -which isa highly nonlinear singular differential equation [2], the solution of composite and non-composite fractional deferential equations [3], predicting and representing the multiplicity of s”