Solution of twelfth-order boundary value problems by variational iteration technique

2008 ◽  
Vol 28 (1-2) ◽  
pp. 123-131 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Variational Iteration ◽  
Iteration Technique

scholarly journals Effects of Nonlinearity on the Variational Iteration Solutions of Nonlinear Two-Point Boundary Value Problems with Comparison with Respect to Finite Element Analysis

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
MehmetTarık Atay ◽  
SafaBozkurt Coşkun
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Burger Equation ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Point Boundary ◽  
Element Analysis ◽  
Variational Iteration ◽  
Fine Mesh

Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions.

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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