scholarly journals Variational iteration method for solving two-point boundary value problems

2007 ◽  
Vol 207 (1) ◽  
pp. 92-95 ◽  
Author(s):  
Junfeng Lu
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Point Boundary ◽  
Variational Iteration

A Multiple Variational Iteration Method for Nonlinear Two-Point Boundary Value Problems with Nonlinear Conditions

2020 ◽  
Vol 18 (01) ◽  
pp. 2050028
Author(s):  
Asghar Ghorbani ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Boundary Value Problems ◽  
Rate Of Convergence ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Original Method ◽  
Second Order ◽  
Convergence Speed ◽  
Point Boundary ◽  
Variational Iteration

A multiple variational iteration method (VIM) is proposed to effectively solve the second-order nonlinear two-point boundary value problems. For problems where convergence speed of the original VIM is slow or the original method is divergent, the multiple VIM method (MVIM) presented in this paper can readily improve the rate of convergence.

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.

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