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.

VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR HIGHER-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS

2009 ◽  
Vol 06 (04) ◽  
pp. 521-555 ◽  
Author(s):  
SYED TAUSEEF MOHYUD-DIN ◽  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Nonlinear Boundary ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Variational Iteration ◽  
Adomian’S Polynomials

In this paper, we apply variational iteration method (VIM) and variational iteration method using Adomian's polynomials for solving nonlinear boundary value problems. The proposed iterative scheme finds the solution without any discretization, linearization, perturbation, or restrictive assumptions. Several examples are given to verify the accuracy and efficiency of the method. We have also considered an example where the proposed VIM is not reliable.

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.

The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

2008 ◽  
Vol 63 (12) ◽  
pp. 745-751 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Ahmad Shirzadi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Functional Equations ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Eighth Order ◽  
Variational Iteration ◽  
Special Cases

The variational iteration method, a well-known method for solving functional equations, is employed to solve a class of eighth-order boundary-value problems, which govern scientific and engineering experimentations. Some special cases of the mentioned equations are solved as examples to illustrate the ability and reliability of the method. The results reveal that the method is very effective and convenient.

Dual solutions for nonlinear boundary value problems by the variational iteration method

2017 ◽  
Vol 27 (1) ◽  
pp. 210-220 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Dual Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Content Type ◽  
Variational Iteration ◽  
Linear And Nonlinear

Purpose The purpose of this paper is to use the variational iteration method (VIM) for studying boundary value problems (BVPs) characterized with dual solutions. Design/methodology/approach The VIM proved to be practical for solving linear and nonlinear problems arising in scientific and engineering applications. In this work, the aim is to use the VIM for a reliable treatment of nonlinear boundary value problems characterized with dual solutions. Findings The VIM is shown to solve nonlinear BVPs, either linear or nonlinear. It is shown that the VIM solves these models without requiring restrictive assumptions and in a straightforward manner. The conclusions are justified by investigating many scientific models. Research limitations/implications The VIM provides convergent series solutions for linear and nonlinear equations in the same manner. Practical implications The VIM is practical and shows more power compared to existing techniques. Social implications The VIM handles linear and nonlinear models in the same manner. Originality/value This work highlights a reliable technique for solving nonlinear BVPs that possess dual solutions. This paper has shown the power of the VIM for handling BVPs.

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