Finding multiple solutions of nonlinear problems by means of the homotopy analysis method

Journal of Hydrodynamics

Volumn 18, Issue 3 SUPPL., 2006, Pages 54-56

  LIAO, Shijun ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

HAM; multiple solutions; nonlinear

Indexed keywords

HYDRODYNAMICS; NONLINEAR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

HOMOTOPY ANALYSIS METHOD (HAM); MULTIPLE SOLUTIONS; PERMEABLE PLATES;

BOUNDARY LAYER FLOW;

EID: 34247198283     PISSN: 10016058     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1001-6058(06)60030-9     Document Type: Article

References (18)

1. Liao S.J. The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Dissertation (1992), Shanghai Jiao Tong University
2. Lyapunov A.M. (1892)General Problem on Stability of Motion (1992), Taylor & Francis, London (English translation)
3. Karmishin A.V., Zhukov A.T., and Kolosov V.G. Methods of Dynamics Calculation and Testing for Thin-walled Structures (1990), Mashinostroyenie, Moscow (In Russian)
4. Adomian G. Nonlinear stochastic differential equation. J. Math. Anal. And Applic. Vol. 55 (1976) 441-452
5. Liao S.J. Beyond Perturbation: Introduction to the Homotopy Analysis Method (2003), Chapman & HallCRC Press, Boca Raton
6. He J.H. Homotopy Perturbation Technique, Comput. Methods Appl. Mech. Engineering vol. 178 (1999) 257-262
7. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method". Applied Mathematics and Computation Vol. 169 Issue 2 (2005) 1186-1194
8. Liao S.J. An approximate solution technique which does not depend upon small parameters: a special example. International Journal of Nonlinear Mechanics 30 (1995) 371-380
9. Liao S.J. An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics. International Journal of Nonlinear Mechanics Vol. 32 No. 5 (1997) 815-822
10. Liao S.J. An explicit, totally analytic approximation of Blasius' viscous flow problems. International Journal of Non-Linear Mechanics Vol. 34 No. 4 (1999) 759-778
11. Liao S.J. "On the homotopy analysis method for nonlinear problems". Applied Mathematics and Computation vol. 147/2 (2003) 499-513
12. Liao S.J. "A new branch of solutions of boundary-layer flows over an impermeable stretched plate". Int. J. Heat and Mass Transfer 48/12 (2005) 2529-2539
13. S.J. Liao and E. Magyari, "Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones", ZAMP, in press.
14. S.J. Liao, "Series solutions of unsteady boundary-layer flows over a stretching flat plate", Studies in Applied Mathematics, in press.
15. S.J. Liao, J. Su and A.T. Chwang, "Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body", Int. J. Heat and Mass Transfer, in press.
16. H. Xu, S.J. Liao and I. Pop, "Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate", European Mechanics- B Fluid, in press.
17. H. Xu and S.J. Liao, "Series solutions of unsteady MHD flows above a rotating disk", Meccanica, in press.
18. Banks W.H.H. Similarity solutions of the boundaryplayer equations for a stretching wall. J. de Mechanique theorique et appliquee Vol. 2 (1983) 375-392