Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Boundary Value Problems

In this article, the variational iteration algorithm-I with an auxiliary parameter (VIA-I with AP) is elaborated to initial and boundary value problems. The effectiveness, absence of difficulty and accuracy of the proposed method is remarkable and its tractability is well suitable for the use of these type of problems. Some examples have been given to show the effectiveness and utilization of this technique. A comparison of variational iteration algorithm-I (VIA-I) along VIA-I with AP has been carried out. It can be seen that this technique is more appropriate than as VIA-I.

Second-order two-point boundary value problems using the variational iteration algorithm-II

International Journal of Computer Mathematics ◽

10.1080/00207160.2010.496481 ◽

2011 ◽

Vol 88 (6) ◽

pp. 1201-1207 ◽

Cited By ~ 4

Author(s):

Boying Wu ◽

Xiuying Li

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Second Order ◽

Iteration Algorithm ◽

Point Boundary ◽

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

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-008-0081-0 ◽

2008 ◽

Vol 28 (1-2) ◽

pp. 123-131 ◽

Cited By ~ 5

Author(s):

Muhammad Aslam Noor ◽

Syed Tauseef Mohyud-Din

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Variational Iteration ◽

Iteration Technique

Variational iteration method for solving twelfth-order boundary-value problems using He’s polynomials

Computational Mathematics and Modeling ◽

10.1007/s10598-010-9068-4 ◽

2010 ◽

Vol 21 (2) ◽

pp. 239-251 ◽

Cited By ~ 1

Author(s):

Muhammad Aslam Noor ◽

Syed Tauseef Mohyud-Din

Keyword(s):

Boundary Value Problems ◽

Iteration Method ◽

Boundary Value ◽

Variational Iteration ◽

He’S Polynomials

WITHDRAWN: Variational iteration method for solving the boundary value problems 3 of integro-differential equations systems

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2009.03.031 ◽

2009 ◽

Author(s):

Onur Karaoğlu ◽

Yıldıray Keskin ◽

Galip Oturanç

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Iteration Method ◽

Boundary Value ◽

Application of He's variational iteration method to the fifth-order boundary value problems

Journal of Physics Conference Series ◽

10.1088/1742-6596/96/1/012185 ◽

2008 ◽

Vol 96 ◽

pp. 012185

Author(s):

S Shen

Keyword(s):

Boundary Value Problems ◽

Iteration Method ◽

Boundary Value ◽

Variational Iteration ◽

He’S Variational Iteration Method ◽

Fifth Order

The numerical solution of fifth-order boundary value problems by the variational iteration method

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2009.03.073 ◽

2009 ◽

Vol 58 (11-12) ◽

pp. 2347-2350 ◽

Cited By ~ 13

Author(s):

Juan Zhang

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Iteration Method ◽

Boundary Value ◽

Variational Iteration ◽

Fifth Order

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

Mathematical Problems in Engineering ◽

10.1155/2008/857296 ◽

2008 ◽

Vol 2008 ◽

pp. 1-10 ◽

Cited By ~ 5

Author(s):

MehmetTarık Atay ◽

SafaBozkurt Coşkun

Keyword(s):

Finite Element ◽

Boundary Value Problems ◽

Nonlinear Term ◽

Burger Equation ◽

Boundary Value ◽

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.

Variational Iteration Decomposition Method for Solving Eighth-Order Boundary Value Problems

Differential Equations and Nonlinear Mechanics ◽

10.1155/2007/19529 ◽

2007 ◽

Vol 2007 ◽

pp. 1-16 ◽

Cited By ~ 16

Author(s):

Muhammad Aslam Noor ◽

Syed Tauseef Mohyud-Din

Keyword(s):

Boundary Value Problems ◽

Decomposition Method ◽

Boundary Value ◽

Convergent Series ◽

Nonlinear Boundary Value Problems ◽

Eighth Order ◽

Numerical Work ◽

Analytical Technique ◽

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.