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Homotopy analysis method: A new analytic method for nonlinear problems. (English) Zbl 1126.34311

34A45Theoretical approximation of solutions of ODE
Full Text: DOI
[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. · Zbl 0754.76065
[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. · Zbl 0882.65108 · 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. · Zbl 0863.76037 · 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. · Zbl 39.0803.02
[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). · Zbl 61.0924.01
[13] L. Howarth, On the solution of the laminar boundary layer equations,Proc. Roy. Soc. London A,164 (1938), 547--579. · Zbl 64.1452.01 · doi:10.1098/rspa.1938.0037