scholarly journals Variational Iteration Method for Solving Boundary Value Problems of Fractional Order

2019 ◽  
Vol 00 (2) ◽  
pp. 59-64
Author(s):  
Fadhel S. Fadhel ◽  
◽  
Saif Al-Deen M. Jameel ◽  
Keyword(s):  
Boundary Value Problems ◽  
Fractional Order ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Variational Iteration

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 Initial and Boundary Value Problems Using He's Polynomials

2010 ◽  
Vol 2010 ◽  
pp. 1-28 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim ◽  
M. M. Hosseini
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
User Friendly

This paper outlines a detailed study of the coupling of He's polynomials with correction functional of variational iteration method (VIM) for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He's polynomials (VIMHP) is very efficient, easier to implements, and more user friendly. Several examples are given to reconfirm the efficiency of the proposed VIMHP.

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