Homotopy analysis method: A new analytic method for nonlinear problems
- 541 Downloads
In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Different from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.
Key wordsnonlinear analytic technique strong nonlinearity homotopy topology
Unable to display preview. Download preview PDF.
- S. J. Liao, The homotopy analysis method and its applications, in mechanics, Ph. D. Dissertation, Shanghai Jiaotong University (1992).Google Scholar
- S. J. Liao, A kind of linear invariance under homotopy and some simple applications of it in mechanics, Bericht Nr. 520, Institut fuer Schiffbau der Universitaet Hamburg (1992).Google Scholar
- S. J. Liao, Application of process analysis method to the solution of 2D non-linear progressive gravity waves,J. Ship Research,36 (1992) 30–37.Google Scholar
- S. J. Liao,Boundary Elements, X VII, Computational Mechanics Publications Southampton (1995), 67–74.Google Scholar
- S. J. Liao, Homotopy analysis method and its applications in mathematics.Journal of Basic Science and Engineering,5, 2 (1997), 111–125.Google Scholar
- H. Blasius, Grenzschichten in Flüessigkeiten mit kleiner Reibung.Z. Math u. Phys.,56 (1908), 1–37.Google Scholar
- L. Howarth, On the calculation of steady flow in the boundary layer near the surface of a cylinder in a stream,ARC RM,1632 (1935).Google Scholar