Homotopy Analysis Method in Nonlinear Differential Equations

By Shijun Liao. 2012

1,080 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c3bb7813cd0bfb0309ce57d0f13cb42f1ff0ceed

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Citations in the corpus

Study of Natural Convection MHD Nanofluid by Means of Single and Multi-Walled Carbon Nanotubes Suspended in a Salt-Water Solution (2015, methodology): “0 [33], [34] based on the homotopy analysis method, an extensively validated, highly efficient analytical technique which has been successfully applied in the past two decades to provide reliable results in an acceptable and accurate way to deal with highly nonlinear equations in science, finance an”
Optimal homotopy analysis method for the non-isothermal reaction–diffusion model equations in a spherical catalyst (2018, methodology): “where Dm−1 [25], is given by Dm−1[ f (φ)] = 1 (m − 1)! ∂m−1 ∂qm−1 f ( ∞ ∑ k=0 ykq k ) ∣∣ q=0.”
Optimal execution with non-linear transient market impact (2014, methodology): “Recent results given by Turkyilmazoglu [48] and Liao [33] show how to compute the homotopy-derivative of any smooth function.”
Solving a model for the evolution of smoking habit in Spain with homotopy analysis method (2013, methodology): “To determine the best value of h we have used the so-called optimal convergencecontrol parameter technique [10,11].”
An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method (2016, methodology): “A treatment of the nonlinear eigenvalue problem (24) was presented in [8] and so we closely follow that source in our HAM approach.”
The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection (2016, methodology): “This method is particularly suitable for strongly nonlinear problems (Liao 2003, 2012; Ellahi 2013).”
MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects (2016, methodology): “Homotopy analysis method [40-55] has been implemented for the development of convergent series solution for velocity, temperature and nanoparticle concentration.”