Saeid Abbasbandy talks with
ScienceWatch.com and answers a few questions about
this month's New Hot Paper in the field of
Mathematics.
Article Title: Homotopy analysis method for
quadratic Riccati differential equation
Authors: Tan,
Y;Abbasbandy,
S
Journal: COMMUN NONLINEAR SCI NUMER SI
Volume: 13
Issue: 3
Page: 539-546
Year: JUN 2008
* Imam Khomeini Int Univ, Dept Math, Ghazvin 34194,
Iran.
* Imam Khomeini Int Univ, Dept Math, Ghazvin 34194,
Iran.
(addresses have been truncated)
Why do you think your paper is highly
cited?
In this paper, a new and powerful method, i.e., the Homotopy analysis
method (HAM) is used for solving a famous differential equation. We show
that the solution obtained by an older method like the Adomian
decomposition method (ADM), is a special case of the HAM solution.
Does it describe a new discovery,
methodology, or synthesis of knowledge?
Yes, this paper describes a new methodology, named the "Homotopy analysis
method" which was first introduced in 1992 by Prof. Shijun J. Liao of the
Shanghai Jiaotong University in Shanghai, P. R. China.
Would you summarize the significance of your
paper in layman's terms?
In this paper, we found the series solution of the quadratic Riccati
equation by HAM and we made a comparison with older methods.
How did you become involved in this research,
and were there any problems along the way?
Before the publication of this paper, I had already published several
papers on the Riccatti equation. I first become acquainted with this method
while in China when, through my studies with Prof. Shijun J. Liao, I began
to concentrate on this area of research.
Where do you see your research leading in the
future?
I will continue my research into this topic and also into the so-called
"Fuzzy Numerical Mathematics." I want to combine HAM with fuzzy numerical
mathematics for solving some fuzzy partial differential equations.
I would like to thank my University for their continued financial support
for my research and also I'd like to thank my Ph.D. supervisor, Prof.
Esmail Babolian, of the Institute for Studies in Theoretical Physics and
Mathematics (IPM) in Tehran, Iran.
Saeid Abbasbandy
Professor of Applied Mathematics
Department of Mathematics
Imam Khomeini International University
Ghazvin, Iran Web