A study on the convergence of variational iteration method

Variational iteration method has been widely used to handle linear and nonlinear models. The main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper, we present an alternative approach of the method then we study the converge...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 51; no. 9; pp. 1181 - 1192
Main Author: Odibat, Zaid M.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2010
Elsevier
Subjects:
Calculus of variations and optimal control
Convergence
Error estimate
Exact sciences and technology
Hilbert space
Lagrange multiplier
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Ordinary differential equations
Sciences and techniques of general use
Series solution
Variational iteration method
Variational iteration method
Lagrange multiplier
Hilbert space
Error estimate
Series solution
Convergence
Error estimation
Differential equation
Initial value problem
Optimization method
Iteration
Partial differential equation
Linear model
Non linear equation
Numerical analysis
Sufficient condition
Boundary value problem
Applied mathematics
Non linear model
Variational calculus
Mathematical model
Computer aided analysis
Method study
Mathematical programming
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:Variational iteration method has been widely used to handle linear and nonlinear models. The main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper, we present an alternative approach of the method then we study the convergence of the method for nonlinear differential equations. Our emphasis is to address the sufficient condition for convergence and the error estimate. Simple approaches of variational iteration method to nonlinear ordinary, partial and fractional differential equations are presented and the convergence results are briefly discussed. Some examples are investigated to verify convergence results and to illustrate the efficiency of the method. The basic ideas described in this paper are expected to be further employed to handle nonlinear models.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2009.12.034