A Novel Iterative Scheme and Its Application to Differential Equations

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed...

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Bibliographic Details
Published in:TheScientificWorld Vol. 2014; no. 2014; pp. 1 - 4
Main Authors: Khan, Yasir, Šmarda, Zdenĕk, Naeem, F.
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2014
John Wiley & Sons, Inc
Wiley
Subjects:
Algorithms
Colleges & universities
Cybernetics
Decomposition
Differential equations
Electrical engineering
Iterative methods (Mathematics)
Lagrange multiplier
Lagrangian functions
Mathematical research
Mathematics
Methods
Variational principles
ISSN:2356-6140, 1537-744X, 1537-744X
Online Access:Get full text
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Summary:The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.
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Academic Editors: H. Jafari and C. M. Khalique
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/605376