Variational iteration method for solving nonlinear boundary value problems

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.

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-10-2015-0442 ◽

2017 ◽

Vol 27 (1) ◽

pp. 210-220 ◽

Cited By ~ 9

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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An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

Mathematical Problems in Engineering ◽

10.1155/2008/394103 ◽

2008 ◽

Vol 2008 ◽

pp. 1-13 ◽

Cited By ~ 13

Author(s):

A. Barari ◽

M. Omidvar ◽

D. D. Ganji ◽

Abbas Tahmasebi Poor

Keyword(s):

Fluid Mechanics ◽

Exact Solutions ◽

Boundary Value Problems ◽

Iteration Method ◽

Structural Engineering ◽

Nonlinear Boundary ◽

Boundary Value ◽

Variational Iteration Method ◽

Nonlinear Boundary Value Problems ◽

Linear And Nonlinear

Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.

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