Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 14, Issue 4, Pages 983-997Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2008.04.013
Keywords
Nonlinear equations; Series solution; Homotopy analysis method
Categories
Funding
- National Natural Science Foundation of China [10572095]
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We describe, very briefly, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers. Definitions of some new concepts such as the homotopy-derivative, the convergence-control parameter and so on, are given to redescribe the method more rigorously. Some lemmas and theorems about the homotopy-derivative and the deformation equation are proved. Besides, a few open questions are discussed, and a hypothesis is put forward for future studies. (c) 2008 Elsevier B.V. All rights reserved.
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