Ph.D. Dissertation
Liao, S.J.: Proposed homotopy analysis techniques for the
solution of nonlinear problems. Ph.D. dissertation, Shanghai Jiaotong
University, 1992.
Books
Liao, S.J.: Beyond Perturbation –
Introduction to the Homotopy Analysis Method. Chapman & Hall/CRC,
Boca Raton, 2003. ( Booking )
Liao, S.J.: Homotopy Analysis Method in
Nonlinear Differential Equations. Springer & Higher Education Press, Heidelberg,
2012. ( Booking )
Selected Journal Articles
1. Liao, S.J.: An approximate solution technique which does
not depend upon small parameters: a special example. Int. J. Non-Linear Mechanics, 30:
371-380 (1995). [ PDF ]
2. Liao, S.J.: An approximate solution technique which does
not depend upon small parameters (Part 2): an application in fluid mechanics. Int.
J. Non-Linear Mechanics, 32:
815-822 (1997). [ PDF ]
3. Liao, S.J.: An explicit, totally analytic approximation
of Blasius’ viscous flow problems. Int.
J. Non-Linear Mechanics, 34(4):
759-778 (1999). [ PDF ]
4. Liao, S.J.: A uniformly valid analytic solution of 2D
viscous flow past a semi-infinite flat plate. J. Fluid Mechanics, 385:
101-128 (1999). [ PDF ]
5. Liao, S.J. and Campo, A.: Analytic solutions of the
temperature distribution in Blasius viscous flow problems. J. Fluid Mechanics, 453:
411-425 (2002). [ PDF ]
6. Liao, S.J.: On the analytic solution of
magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mechanics, 488: 189-212 (2003). [ PDF ]
7. Liao, S.J.: On the homotopy analysis method for nonlinear
problems. Applied Mathematics and Computation, 147: 499-513 (2004). [ PDF ]
8. Liao, S.J.: A new branch of solutions of boundary-layer
flows over an impermeable stretched plate. Int. J. Heat and Mass Transfer,
48: 2529-2539 (2005). [ PDF
]
9. Liao, S.J.: Series solutions of unsteady boundary-layer
flows over a stretching flat plate. Studies
in Applied Mathematics, 117:
239-263 (2006). [ PDF ]
10. Liao, S.J. and Tan, Y.: A general approach to obtain series solutions of
nonlinear differential equations. Studies
in Applied Mathematics, 119:
297-354 (2007). [ PDF ]
11. S.J. Liao,
“Notes on the homotopy analysis method: some definitions and theorems”, Communications in Nonlinear Science and
Numerical Simulation, vol. 14, pp. 983-997, 2009. [ PDF
]
12. Xu, H., Lin, Z.L., Liao, S.J., Wu, J.Z. and Majdalani, J.: Homotopy-based solutions of the Navier–Stokes equations for a porous
channel with orthogonally moving walls. Physics of Fluids, 22(5): 053601 (2010). [ PDF
]
13. Li, Y.J., Nohara, B.T. and
Liao, S.J.: Series solutions of coupled Van
der Pol equation by means of homotopy analysis method.
J. Mathematical Physics, 51: 063517
(2010). [ PDF ]
14. Liao, S.J.: An optimal homotopy-analysis approach for strongly nonlinear
differential equations. Communications in Nonlinear Science and Numerical
Simulation, 15:2003-2016 (2010). [ PDF
]
15. 廖世俊，“超越摄动：同伦分析方法基本思想及其应用”，《力学进展》，２００８年，第３８卷，第１期，１-３４页（中文综述论文）[ PDF ]
16. 廖世俊，“同伦分析方法：求解强非线性问题的一个新途径”，《科学观察》，２００９年，第４卷，第５期，４８-４９页（热点研究论文特约稿）[ PDF
]
17. 廖世俊，“同伦分析方法：研究背景和现状”，《科学观察》，２０１１年，第６卷，第６期，５５-５８页（热点研究论文特约稿）[ PDF
]
18. Liao, S.J.: On the reliability of computed
chaotic solutions of non-linear differential equations. Tellus, 61(A):
550-564 (2009). [ PDF
] (arXiv:0901.2986)
19. Liao, S.J.: Chaos –
A bridge from micro-level uncertainty to macroscopic randomness. Communications in Nonlinear Science and Numerical
Simulation. 17: 2564-2569 (2012) [ PDF
] (arXiv:1108.4472).
20. Liao, S.J.: On the
numerical simulation of propagation of micro-level inherent uncertainty for
chaotic dynamic systems. Chaos, Solitons
& Fractals, 47: 1-12 (2013). [PDF]