Homotopy analysis method: Difference between revisions

Revision as of 03:21, 25 May 2012

Revision as of 04:55, 25 May 2012

Line 10:

== References ==

*{{citation | last=Liao | first=S.J. | title=The proposed homotopy analysis technique for the solution of nonlinear problems | publisher=PhD thesis, Shanghai Jiao Tong University | year=1992 }}

*{{citation | last=Liao | first=S.J. | title=Beyond Perturbation: Introduction to the Homotopy Analysis Method | publisher=Chapman & Hall/ CRC Press | ___location=Boca Raton | year=2003 | isbn=1-58488-407-X }}[http://www.amazon.com/Beyond-Perturbation-Introduction-Mechanics-Mathematics/dp/158488407X]

*{{citation | last=Liao | first=S.J. | title=Homotopy Analysis Method in Nonlinear Differential Equation| publisher=Springer & Higher Education Press| ___location=Berlin & Beijing | year=2012 | isbn=978-3642251313(3642251315)}}For Details see [http://www.amazon.com/Homotopy-Analysis-Nonlinear-Differential-Equations/dp/3642251315]

*{{citation | last=Liao | first=S.J. | title=A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate| journal=J. Fluid Mechanics| volume=385 |pages=101-128 | year=1999 }}

Line 18:

*{{citation | last=Liao | first=S.J. | title=An optimal homotopy-analysis approach for strongly nonlinear differential equations | journal=Communications in Nonlinear Science and Numerical Simulation| volume=15| pages=2003–2016| year=2010 }}Download from site [http://numericaltank.sjtu.edu.cn/publication.htm]

*{{citation | last=Liao | first=S.J. | title=On the homotopy analysis method for nonlinear problems | url=http://numericaltank.sjtu.edu.cn/paper/AMC-HAM-2004.pdf | journal=Applied Mathematics and Computation | volume=147 | issue=2 | pages=499–513 | year=2004 | doi=10.1016/S0096-3003(02)00790-7}}

*{{citation | last1=Liao | first1=S.J. | last2=Tan | first2=Y. | title=A general approach to obtain series solutions of nonlinear differential equations | url=http://numericaltank.sjtu.edu.cn/paper/SAM-2007-Vol%20119%20pp%20297-355.pdf | journal=Studies in Applied Mathematics | volume=119 | pages=297–354 | year=2007 | doi=10.1111/j.1467-9590.2007.00387.x | issue=4 }}; see also this [[Mathematica]] [http://numericaltank.sjtu.edu.cn/code/Gelfand2D.nb notebook file]

*{{citation | last=Liao | first=S.J. | title=Notes on the homotopy analysis method: some definitions and theorems |url=http://numericaltank.sjtu.edu.cn/paper/LIAO-CNSNS-2009%20Notes%20on%20HAM.pdf | journal=Communications in Nonlinear Science and Numerical Simulation | volume=14 | pages=983–997 | year=2009 | doi=10.1016/j.cnsns.2008.04.013 |bibcode = 2009CNSNS..14..983L | issue=4}}

*{{citation | last1=Xu | first1=H. | last2=Lin | first2=Z.L.| last3=Liao | first3=S.J.|last4=Wu | first4=J.Z.| last5=Majdalani | first5=J.|title=Homotopy-based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls| url=http://numericaltank.sjtu.edu.cn/paper/SAM-2007-Vol%20119%20pp%20297-355.pdf | journal=Physics of Fluids| volume=22 | year=2010 | issue=5 }}; see also this [http://numericaltank.sjtu.edu.cn/publication.htm]

*{{citation | last1=Li | first1=Y.J. | last2=Nohara | first2=B.T.| last3=Liao | first3=S.J.|title= Series solutions of coupled Van der Pol equation by means of homotopy analysis method| journal=J. Mathematical Physics| volume=51 | year=2010 | issue=063517}}; see this [http://numericaltank.sjtu.edu.cn/publication.htm]

*{{citation | last=廖| first=世俊| title=同伦分析方法：求解强非线性问题的一个新途径 | journal=力学进展| volume=38 | pages=1–34 | year=2008| issue=1}}