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

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
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.

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.

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 Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ishfaq Ahmad Ganaie ◽  
Shelly Arora ◽  
V. K. Kukreja
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Spline Method ◽  
Orthogonal Collocation ◽  
Nonlinear Boundary Value Problems ◽  
B Spline ◽  
Linear And Nonlinear ◽  
Volume Method

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

scholarly journals Boundary value problems for differential equations with reflection of the argument

1985 ◽  
Vol 8 (1) ◽  
pp. 151-163 ◽  
Author(s):  
Joseph Wiener ◽  
A. R. Aftabizadeh
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

Linear and nonlinear boundary value problems for differential equations with reflection of the argument are considered.

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