000 03372nam a22004695i 4500
001 978-3-642-25132-0
003 DE-He213
005 20140220083305.0
007 cr nn 008mamaa
008 120621s2012 gw | s |||| 0|eng d
020 _a9783642251320
_9978-3-642-25132-0
024 7 _a10.1007/978-3-642-25132-0
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aLiao, Shijun.
_eauthor.
245 1 0 _aHomotopy Analysis Method in Nonlinear Differential Equations
_h[electronic resource] /
_cby Shijun Liao.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aX, 400p. 50 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aBasic Ideas -- Systematic Descriptions -- Advanced Approaches -- Convergent Series For Divergent Taylor Series -- Nonlinear Initial Value Problems -- Nonlinear Eigenvalue Problems -- Nonlinear Problems In Heat Transfer -- Nonlinear Problems With Free Or Moving Boundary -- Steady-State Similarity Boundary-Layer Flows -- Unsteady Similarity Boundary-Layer Flows -- Non-Similarity Boundary-Layer Flows -- Applications In Numerical Methods.
520 _a"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM).  Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters.  In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution.  Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts.  Part I provides its basic ideas and theoretical development.  Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications.  Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves.  New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM.  Mathematica codes are freely available online to make it easy for readers to understand and use the HAM.    This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiaotong University, is a pioneer of the HAM.   
650 0 _aMathematics.
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aNonlinear Dynamics.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aOrdinary Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642251313
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-25132-0
912 _aZDB-2-SMA
999 _c102384
_d102384