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Homotopy analysis method: A new analytic method for nonlinear problems. (English) Zbl 1126.34311
MSC:
34A45Theoretical approximation of solutions of ODE
References:
[1]S. J. Liao, The homotopy analysis method and its applications, in mechanics, Ph. D. Dissertation, Shanghai Jiaotong University (1992).
[2]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).
[3]S. J. Liao, A second-order approximate analytical solution of a simple pendulum by the process analysis method.J. Applied Mechanics,14 (1992), 1173–1191.
[4]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.
[5]S. J. Liao, A kind of approximate solution technique which does not depend upon small parameters: a special example,Int. J. Non-Linear Mechanics.30 (1995), 371–380. · Zbl 0837.76073 · doi:10.1016/0020-7462(94)00054-E
[6]S. J. Liao, A kind of approximate solution technique which does not depend upon small parameters (2): an application in fluid mechanics.Int. J. Non-Linear Mechanics,32, 5 (1997), 815–822. · Zbl 1031.76542 · doi:10.1016/S0020-7462(96)00101-1
[7]S. J. Liao,Boundary Elements, X VII, Computational Mechanics Publications Southampton (1995), 67–74.
[8]S. J. Liao, High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators,Int. J. Numerical Methods in Fluids,23 (1996), 739–751. · doi:10.1002/(SICI)1097-0363(19961030)23:8<739::AID-FLD390>3.0.CO;2-8
[9]S. J. Liao and A. T. Chwang, The general BEM for strongly non-linear problems.Int. J. Numerical Methods in Fluids,23 (1996), 467–483. · doi:10.1002/(SICI)1097-0363(19960915)23:5<467::AID-FLD436>3.0.CO;2-9
[10]S. J. Liao, Homotopy analysis method and its applications in mathematics.Journal of Basic Science and Engineering,5, 2 (1997), 111–125.
[11]H. Blasius, Grenzschichten in Flüessigkeiten mit kleiner Reibung.Z. Math u. Phys.,56 (1908), 1–37.
[12]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).
[13]L. Howarth, On the solution of the laminar boundary layer equations,Proc. Roy. Soc. London A,164 (1938), 547–579. · Zbl 02519421 · doi:10.1098/rspa.1938.0037