**Welcome to Dr. Shijun Liao's homepage**

**You are the
visitor since March 1st, 2009 **

Dr. Shijun LIAO

Cheung Kong
Professor

School of
Naval Architecture, Ocean and Civil Engineering

800 Dongchuan Road,
Shanghai 200240,

Email: sjliao@sjtu.edu.cn

Phone: 0086-21-3420 4445
(O)

FAX: 0086-21-3420 4445 (O)

l Nonlinear Mechanics

l Computational Fluid Dynamics (CFD)

l Applied Mathematics

l Ocean Engineering

Shijun Liao, Beyond
Perturbation: Introduction to the Homotopy Analysis Method, Chapman &
Hall/CRC,

Ø
**MATHEMATICA Codes for Chapters 2, 6, 7, 8, and 9. (free
download)**

Ø
**Maple Codes for Chapters 2, 6, 7, 8, 9, 10, 11, 12 and 13. (All the Maple codes are provided
by Miss Pei Yang from
East China Normal University. We express our grateful thanks to Miss Yang.)**

Ø
**BOOK REVIEWS:**

²
“*This book deals with a very interesting mathematical technique that is rather powerful. An excellent
reference to researchers, engineers, and interested individuals in helping them
tackle nonlinear problems in an analytical fashion. A good subject index and an
outstanding list of bibliography with 136 references cited. Very well written and is relatively easy to
follow to the mathematically literate person. I highly
recommend that it be acquired by interested individuals and
libraries throughout*.” -

² “*This monograph offers the opportunity
to explore the details of the valuable new
approach both in the theory and on many
interesting examples. It will be useful to specialists working in
applied nonlinear analysis*.” -

1.
S.J. Liao, “Proposed homotopy analysis techniques for the solution of nonlinear
problems”, ** Ph.D. dissertation**,

2.
S. J. Liao, “An approximate solution technique which does not depend upon
small parameters: a special example”,** International
Journal of Nonlinear Mechanics**, **30**,
371-380, 1995.

3.
S. J. Liao,
“An approximate solution technique which does not depend upon
small parameters (Part 2): an application in fluid mechanics”,**International Journal of Nonlinear
Mechanics**, Vol. 32, No. 5, pp. 815-822, 1997.

4.
S. J. Liao,
“An explicit, totally analytic approximation of Blasius’ viscous flow problems”, **International
Journal of Non-Linear Mechanics**, Vol. 34, No. 4, pp. 759-778, 1999.

5.
S. J. Liao, “A uniformly valid
analytic solution of 2D viscous flow past a semi-infinite flat plate”, **Journal of Fluid Mechanics****,** Vol. 385, pp.
101-128, 1999. ** **

6.
S. J. Liao and A. Campo, “Analytic
solutions of the temperature distribution in Blasius
viscous flow problems”, **Journal
of Fluid Mechanics**, Vol. 453, pp. 411-425, 2002.

7.
S. J. Liao,
“On the analytic solution of magnetohydrodynamic
flows of non-Newtonian fluids over a stretching sheet”, **Journal of Fluid Mechanics**, vol. 488, pp.
189-212, 2003.

8.
S. J. Liao
and K. F. Cheung, “Homotopy analysis of nonlinear progressive waves in deep water”, **J. Engineering Mathematics**,
vol. 45, No. 2, pp. 105-116, 2003.

9.
S. J. Liao,
“An explicit analytic
solution to the Thomas-Fermi equation”,
**Applied Mathematics and
Computation**, vol. 144, pp. 495-506,
2003.

10.
S. J. Liao,
“A new analytic algorithm of Lane-Emden type equations”, **Applied Mathematics and Computation**, vol. 142, No.1, pp. 1-16, 2003.

11.
S. J. Liao,
“On the homotopy
analysis method for nonlinear problems”, **Applied Mathematics and Computation**, vol. 147/2, pp. 499-513, 2004.

12.
S. J. Liao,
“An analytic approximate approach for free oscillations of self-excited
systems”, **Int. J. Non-Linear Mech.**, Vol. 39, No.2, pp.
271-280, 2004.

13.
S. J. Liao,
“A challenging nonlinear
problem for numerical techniques”, **J. Computational and Applied Mathematics**, vol. 181,
pp.467-472, 2005.

14.
S. J. Liao,
“A new branch of solutions
of boundary-layer flows over an impermeable stretched plate”, **Int.
J. Heat and Mass Transfer**, vol. 48, pp. 2529-2539, 2005.

15.
S. J. Liao,
“Comparison
between the homotopy analysis method and homotopy perturbation method”, **Applied Mathematics and
Computation**, Vol. 169, Issue 2, Pages 1186-1194, 2005.

16.
H. Xu and S. J. Liao,
“Analytic solutions of magnetohydrodynamic
flows of non-Newtonian fluids caused by an impulsively stretching plate”, **Journal
of Non-Newtonian Fluid Mechanics**, vol. 129, pp. 46-55, 2005.

17.
S. J. Liao, “Series solutions of unsteady
boundary-layer flows over a stretching flat plate”, **Studies in Applied Mathematics**, Vol. 117, Issue 3, 2006.

18.
S. J. Liao,
“An analytic solution of
unsteady boundary-layer flows caused by an impulsively stretching plate”, **Communications
in Nonlinear Science and Numerical Simulation**, Volume 11, Issue 3, pp.
326-339, 2006.

19.
S. J. Liao,
J. Su and A.T. Chwang, “Series solutions for a nonlinear model of
combined convective and radiative cooling of a
spherical body”, **Int. J. Heat and Mass Transfer**, vol. 49, pp. 2437-2445,
2006.

20.
S. J. Liao and
E. Magyari, “Exponentially decaying
boundary layers as limiting cases of families of algebraically decaying ones”, **Z. angew. Math. Phys**. (**ZAMP),** Volume 57, Number 5, 777 – 792, 2006.

21.
H. Xu, S. J. Liao and
I. Pop, “Series solution of unsteady boundary layer flow of a micropolar
fluid near the forward stagnation point of a plane surface”, **Acta**** Mechanica**,
2006.

22. S.J. Liao and Y. Tan, “A general
approach to obtain series solutions of nonlinear differential equations”, **Studies in Applied Mathematics**, Vol. 119, pp. 297-354, 2007.

23. J. Cheng, S.J. Liao, R.N. Mohapatra and K. Vajravelu,
“Series solutions of Nano-boundary-layer
flows by means of the homotopy analysis method”, **Journal of Mathematical Analysis and
Applications**, 343(1), pp. 233-245, 2008.

24. S.J. Liao, “Beyond perturbation: a review on the homotopy analysis method and its applications”, **Advance in
Mechanics**, Vol. 153, No.1, pp. 1-34, 2008.(in Chinese)

25. J. Cheng,
J. Cang and S.J. Liao,
“On the interaction of deep water waves and
exponential shear currents”, **Z. angew. Math. Phys.**, 60, pp. 450-478, 2009.

26. X. Hang, Z.L. Lin, S.J. Liao, J.Z. Wu and J. Majdalani,
“Homotopy based solutions of
the Navier-Stokes equations for a porous channel with orthogonally moving walls”,**Physics of Fluids**, 22 (2010, online).(new)

27. S.J. Liao,
“An optimal homotopy-analysis approach for strongly nonlinear differential
equations”, **Communications in Nonlinear Science and Numerical Simulation
**, Volume 15, Issue 8, pp. 2003-2016, 2010.

Foreign visitors： Dr.
S. Abbasbandy Yann
Bouremel

**One of Millennium Problems**: **Navier-Stokes Equation**

l
Chinese Mathematical Society

l
International Mathematical Union (IMU)

l
International Association of Mathematical Physics
(IAMP)

l
European Mathematical Society (EMS)

l
American Mathematical Society (AMS)

l
Society for Industrial and Applied Mathematics
(SIAM)

l
American Society Of Mechanical Engineers (ASME)

l
American Institute of Mathematical Sciences

l
Isaac Newton Institute for Mathematical
Sciences

l
Department of Applied Mathematics and
Theoretical Physics (DAMTP)

l
The Nonlinear Centre, UNIVERSITY of
CAMBRIDGE

l
Centre for Nonlinear Dynamics and its
Applications (at UCL)

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Bristol Centre For Applied
Nonlinear Mathematics

l
Mathematics Institutes,
Centers and Laboratories

l
Science

l
Nature