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.

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.

The Weighted Error Estimation of Finite Element Method for Two-Point Boundary Value Problem

2012 ◽  
Vol 182-183 ◽  
pp. 1571-1574
Author(s):  
Qi Sheng Wang ◽  
Jia Dao Lai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Error Estimation ◽  
Boundary Value ◽  
Point Boundary ◽  
Weighted Error ◽  
Element Method

In this paper, the weighed error estimation of finite element method for the two-point boundary value problems are discussed. Respectively, the norm estimation of the H1 and L2 are obtained.

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.

Sign in / Sign up

Export Citation Format

Share Document