Ji-Huan He talks with
ScienceWatch.com and answers a few questions about
this month's New Hot Paper in the field of
Article Title: Variational iteration method - Some
recent results and new interpretations
Journal: J COMPUT APPL MATH
Year: OCT 1 2007
* Donghua Univ, Coll Sci, 1882 Yanan Xilu Rd, Shanghai
200051, Peoples R China.
* Donghua Univ, Coll Sci, Shanghai 200051, Peoples R China.
Why do you think your paper is highly
This paper is an elementary introduction to the concepts of the variational
iteration method. First, the main concepts in the variational iteration
method, such as the general Lagrange multiplier, restricted variation, and
correction functional, are explained heuristically. Subsequently, the
solution procedure is systematically illustrated, which is helpful for a
beginner. Particular attention is paid throughout the paper to give an
intuitive grasp for the method, and the paper provides a universal approach
to various nonlinear equations—these might be the main reasons for
the higher citation rate.
Does it describe a new discovery, methodology, or
synthesis of knowledge?
Yes, the paper does describe a new application of the Lagrange multipliers,
which are used to construct a correction functional for a nonlinear
equation, and it can be optimally identified using the calculus of
variations, whereby the solution converges quickly into an exact one.
Would you summarize the significance of your paper
in layman's terms?
"The concept of the
restricted variation is the landmark in developing
To fully grasp the identification of the Lagrange multipliers in the
correction functionals requires some knowledge of the calculus of
variations, but the result is changed as we tabulated the identified
results for various different equations in our article: Ji-Huan He and
Xu-Hong Wu: "Variational iteration method: New development and
applications," (Computers & Mathematics with Applications 54:
Anyone who knows nothing of variational theory in mathematics can apply the
method to calculate various nonlinear equations; including nonlinear
ordinary equations, nonlinear partial differential equations, stochastic
equations, differential-difference equations, integral equations,
integral-differential equations, and differential-algebraic equations,
making the method most attractive for a layman.
How did you become involved in this research, and
were there any problems along the way?
The story began in 1997 while defending my Ph.D. thesis entitled: "A New
Approach to Establishing Generalized Variational Principles in Fluids and
C.C. Lin's Constraints". It is well known that it is very difficult to
establish a variational formulation for a fluid problem, and in my thesis
the restricted variation was used to approximately construct variational
formulae for various fluid problems. The concept of the restricted
variation is the landmark in developing the method, and makes the
identification of Lagrange multipliers extremely simpler in the variational
This method can be used to solve various nonlinear problems, but it is
still under development. Unnecessary repeated iteration occurs and this
problem was partly solved in my last publication, Ji-Huan He and Xu-Hong
Wu: "Variational iteration method: New development and applications,"
(Computers & Mathematics with Applications 54: 881-94, 2007).
A number of authors have contributed their considerable efforts to the
development of the method and have suggested various modified versions of
these methods, among which the works of Wazwaz, Ganji, Dehghan, Abbasbandy,
Abdou, Yusufoglu, Bekir, Odibat, Momani, Noorani, Hashim, Soliman,
Mohyud-Din, El-Wakil, Biazar, Coskun, Atay, Javidi, Golbabai, Fa-Zhan Geng
and Lan Xu should receive special emphasis.
Where do you see your research leading in the
The method might find potential applications in difference-differential
equations—a two-variable equation consisting of a coupled ordinary
differential equation and recurrence equation—and in numerical
Professor Ji-Huan He
Modern Textile Institute
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