An optimal homotopy-analysis approach for strongly nonlinear differential equations

By Shijun Liao. 2010

1,062 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f5f16dea02adc8c6e66070983e93e2c985fa97aa

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Citations in the corpus

Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects (2014, neutral): “[37–39], for more details):”
An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method (2016, positive): “It is now well-understood that the success of the HAM is constantly attributed to the so-called convergence control parameter, whose optimum value can be worked out making use of the traditional squared residual error definition after the work of [7], see also [3, 12, 13].”
Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation (2011, neutral): “[28] for more details) are defined as Ef ;m 1⁄4 1 K XK i1⁄40 N f Xm j1⁄40 FjðiDxÞ ! " #2 ; ð4:1Þ Eg;m 1⁄4 1 K XK i1⁄40 N g Xm j1⁄40 GjðiDxÞ ! " #2 ; ð4:2Þ Eh;m 1⁄4 1 K XK i1⁄40 N h Xm j1⁄40 HjðiDxÞ ! " #2 ; ð4:3Þ”
Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media (2014, background): “To choose optimal value of auxiliary parameter, the averaged residual errors (see [53] for more details) are defined as”
Solving a model for the evolution of smoking habit in Spain with homotopy analysis method (2013, methodology): “(47) Since we have calculated the HAM solution with 20 terms, we can obtain the [10, 10] homotopy-Padé approximation.”
An analytic solution of micropolar flow in a porous channel with mass injection using homotopy analysis method (2014, background): “In theory, at the mth-order of approximation, one can define the exact square residual error (Liao, 2010):”
Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration (2014, background): “In order to choose the optimal value of auxiliary parameter ( ), the averaged residual error is introduced as (see [38–40], for more details):”
On the Homotopy Analysis Method for Fractional SEIR Epidemic Model (2014, methodology): “This method has been implemented in many branches of mathematics and engineering, such as unsteady boundary-layer flows over a stretching flat plate (Liao, 2006) and strongly nonlinear differential equation (Liao, 2010).”