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. Z. Liu, M. Oberlack, V. N. Grebenev and S.J. Liao, “Explicit series solution of a closure model for the Von Karman-Howarth equation”, ANZIAM J., 52: 179-202 (2010) [ PDF ]

16. 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 ]

17. 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 ]

18. 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 ]