Basic Ideas of the Homotopy Analysis Method

Shijun Liao ()
Additional contact information
Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 2 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 15-94 from Springer

Abstract: Abstract The basic ideas and all fundamental concepts of the homotopy analysis method (HAM) are described in details by means of two simple examples, including the concept of the homotopy, the flexibility of constructing equations for continuous variations, the way to guarantee convergence of solution series, the essence of the convergence-control parameter c 0, the methods to accelerate convergence, and so on. The corresponding Mathematica codes are given in appendixes and free available online. Beginners of the HAM are strongly suggested to read it first.

Keywords: Computer Algebra System; Auxiliary Parameter; Stable Equilibrium Point; Deformation Equation; Iteration Formula (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25132-0_2

Ordering information: This item can be ordered from
http://www.springer.com/9783642251320

DOI: 10.1007/978-3-642-25132-0_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().