scholarly journals Solution of Singular and Nonsingular Initial and Boundary Value Problems by Modified Variational Iteration Method

2008 ◽  
Vol 2008 ◽  
pp. 1-23 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Suggested Algorithm ◽  
Variational Iteration ◽  
Proposed Modification ◽  
Efficiency And Reliability ◽  
Adomian’S Polynomials ◽  
Modified Variational Iteration Method

We apply the modified variational iteration method (MVIM) for solving the singular and nonsingular initial and boundary value problems in this paper. The proposed modification is made by introducing Adomian's polynomials in the correct functional. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the solution without any discretization, linearization, perturbation, or restrictive assumptions. Several examples are given to verify the efficiency and reliability of the suggested algorithm.

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.

Modified Variational Iteration Method for Integro-Differential Equations and Coupled Systems

2010 ◽  
Vol 65 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Syed Tauseef Mohyud-Din
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Coupled Systems ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Proposed Modification ◽  
Adomian’S Polynomials ◽  
Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method (mVIM) for solving integrodifferential equations and coupled systems of integro-differential equations. The proposed modification is made by the elegant coupling of He’s polynomials and the correction functional of variational iteration method. The proposed mVIM is applied without any discretization, transformation or restrictive assumptions and is free from round off errors and calculation of the so-called Adomian’s polynomials.

scholarly journals Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Fifth Order ◽  
Adomian’S Polynomials

We apply the variational iteration method using He's polynomials (VIMHP) for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007). The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

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