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.

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 Decomposition Method for Solving Eighth-Order Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Nonlinear Boundary Value Problems ◽  
Eighth Order ◽  
Numerical Work ◽  
Analytical Technique ◽  
Variational Iteration

We implement a relatively new analytical technique, the variational iteration decomposition method (VIDM), for solving the eighth-order boundary value problems. The proposed method is an elegant combination of variational iteration method and decomposition method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Numerical work is given to check the efficiency of the method. Comparisons are made to confirm the reliability and accuracy of the technique. The technique can be used as an alternative for solving nonlinear boundary value problems.

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