A reliable iterative method for solving the time-dependent singular Emden-Fowler equations

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Numerical Methods ◽  
Iterative Method ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Time Dependent ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Physical Sciences ◽  
Variational Iteration

AbstractMany problems of physical sciences and engineering are modelled by singular boundary value problems. In this paper, the variational iteration method (VIM) is used to study the time-dependent singular Emden-Fowler equations. This method overcomes the difficulties of singularity behavior. The VIM reveals quite a number of features over numerical methods that make it helpful for singular and nonsingular equations. The work is supported by analyzing few examples where the convergence of the results is observed.

scholarly journals Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Marwan Abukhaled
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Whittaker Functions ◽  
Exponential Integral ◽  
Variational Iteration

The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.

scholarly journals Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Perturbation Method ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Initial Boundary Value

A variational homotopy perturbation method (VHPM) which is based on variational iteration method and homotopy perturbation method is applied to solve the approximate solution of the fractional initial boundary value problems. The nonlinear terms can be easily handled by the use of He's polynomials. It is observed that the variational iteration method is very efficient and easier to implements; illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

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