ISSN Print: 2381-1218  ISSN Online: 2381-1226
Computational and Applied Mathematics Journal  
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Comparison of the Solutions of Singular Flierl Petviashvili and the Lane Emden Equations Via Analytical Techniques
Computational and Applied Mathematics Journal
Vol.5 , No. 1, Publication Date: Jun. 3, 2019, Page: 1-8
798 Views Since June 3, 2019, 609 Downloads Since Jun. 3, 2019
 
 
Authors
 
[1]    

Syeda Zoha Hassan, Department of Mathematics, the University of Lahore Chenab Campus, Gujrat, Pakistan.

[2]    

Muhammad Asif Javed, Department of Mathematics, the University of Lahore Chenab Campus, Gujrat, Pakistan.

[3]    

Sabeen Arshad, Department of Physics, the University of Lahore Chenab Campus, Gujrat, Pakistan.

[4]    

Muhammad Nadeem, Department of Mathematics, the University of Lahore Chenab Campus, Gujrat, Pakistan.

 
Abstract
 

The initiative of this paper is to inaugurate a productive comparison of two techniques Adomians Decomposition Method (ADM) and Variational Iteration Method (VIM) for solving the volterra integro-differential equation form of Flierl Petviashvili (FP) and Lane-Emden (LE) equations. The study gives the notable aspects of the two methods and examines the theoretical supporting framework of Adomians Decomposition Method (ADM) and Compares it with Variational Iteration Method (VIM). The aim of the present attempts to find the computational benefits of both the Adomians Decomposition Method (ADM) and Variational Iteration Method (VIM) for solving physical models of FP and LE equations of first and second kind. The Adomians Decomposition method is shown to easily solve the FP and LE equations for all values of the coefficient α, the decomposition series is used to deal with highly nonlinear terms. The Variational Iteration Method also effectively solved the FP and LE equations of first and second kind, both techniques overcome the singular behavior of equations. But after computational results the Variational Iteration Method show impractical approach due to use of Lagrange Multipliers which are not helpful for generalized case. The Adomians Decomposition method shows more efficiency towards generalized FP and LE equations and applications of these equations describes variety of phenomena’s in fluid mechanics, relativistic mechanics and in chemically reacting system. The conclusions are supported by numerical calculations of these equations.


Keywords
 

Flierl-Petviashvili (FP) Equation, Lane-Emden (LE) equation; Variational Iteration Method (VIM), Adomians Decomposition Method (ADM)


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