Homotopy analysis of nonlinear progressive waves in deep water

By Shijun Liao, Kwok Fai Cheung. 2003

277 citations recorded by the source corpus.

Subfields: Numerical Analysis, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6bb68c57fa7ecbda2e6cd506df8c74fae1ac654c

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In Numerical Analysis

In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

On the relationship between the homotopy analysis method and Euler transform (2010, methodology): “Thereafter, the HAM has been improved step by step [14–20] and has been widely applied in science, engineering and finance [21–29].”
On the analytic solutions of the nonhomogeneous Blasius problem (2005, background): “Several attempts were made to derive an analytical solution of the problem for the case = 0, see [8–11,13–20].”
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet (2003, methodology): “As verified in the author’s previous publications (Liao & Chwang 1998; Liao 1999 a, b, 2003; Liao & Campo 2002; Liao & Cheung 2003), it is the value of the auxiliary parameter which can adjust and control the convergence region and rate of the series given by the homotopy analysis method.”
Dual solutions of boundary layer flow over an upstream moving plate (2008, methodology): “The homotopy analysis method has been successfully applied to many nonlinear problems [16–25].”
Nonlinear progressive waves in water of finite depth — an analytic approximation (2007, methodology): “As demonstrated by Liao and Cheung (2003), the homotopy-Padé approximants give converging results over a considerably large region at the same order of approximation.”
A new branch of solutions of boundary-layer flows over a permeable stretching plate (2007, methodology): “In this paper, a new branch of solutions is found for 1/2 < b < +1 by means of the homotopy analysis method [18–20], which has been successfully applied to solve many nonlinear problems [21–26,28,27].”