Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate

By Shijun Liao. 2006

146 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/80a80f60445d1d68d0221a3a11fb975cbeb74b98

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

In Modeling and Simulation

Citations in the corpus

A General Approach to Obtain Series Solutions of Nonlinear Differential Equations (2007, methodology): “As pointed out by Liao ([13], chapters 2 and 3) and mentioned in Section 2, the initial guess and the auxiliary linear operator must be chosen in such a way that the solutions of the high-order deformation equations exist and do not disobey the solution expression: this is so important in the frame ”
A new branch of solutions of boundary-layer flows over a permeable stretching plate (2007, methodology): “Besides, the HAM has been successfully applied to solve some PDEs, such as the unsteady boundary-layer viscous flows [48], the unsteady non-linear heat transfer problem [49], and so on.”
Homotopy Analysis Method in Nonlinear Differential Equations (2012, methodology): “In this way, the original nonlinear PDE with variable coefficients is transferred into an infinite number of linear ODEs with constant coefficients.”
Solution of Delay Differential Equation by Means of Homotopy Analysis Method (2009, unknown): “of differential equations [8–12].”
Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations (2008, methodology): “Liao pointed out [14,17–20,22] that the convergence of the solution series given by the HAM is determined by h̄, and thus one can always get a convergent series solution by means of choosing a proper value of h̄.”
An explicit solution of the large deformation of a cantilever beam under point load at the free tip (2008, background): “In fact, the HAM [11–15,4–6,8,17–19,1,2] is capable of solving a wide range of nonlinear problems, particularly when the nonlinearity is strong.”
Soliton solutions for the fifth-order KdV equation with the homotopy analysis method (2007, background): “model of combined convective and radiative cooling of a spherical body [12], exponentially decaying boundary layers [13], and unsteady boundary-layer flows over a stretching flat plate [ 14 ].”
Solving nonlinear fractional partial differential equations using the homotopy analysis method (2010, methodology): “The q = 0 and q = 1, give respectively [53–56] v(x, t ; 0) = u0(x, t), v(x, t ; 1) = u(x, t).”
On the Homotopy Analysis Method for Fractional SEIR Epidemic Model (2014, methodology): “THE HOMOTOPY ANALYSIS METHOD (HAM) The principles of the HAM and its applicability for various kinds of differential equations are given in Liao (1992, 1998, 2003, 2004, 2006), El-Ajou et al. (2012) and Abu Arqub et al. (2013a).”
SERIES SOLUTIONS OF NON-LINEAR RICCATI DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER (2009, methodology): “The homotopy analysis method has been successfully applied to many non-linear problems, such as non-linear vibration [24], non-linear water waves [25], viscous flows of non-Newtonian fluids [19,20,26,27], unsteady viscous flows [28], the generalized Hirota–Satsuma coupled KdV equation [22], Thomas–F”
An optimal homotopy-analysis approach for strongly nonlinear differential equations (2010, background): “In fact, the guarantee of the convergence of homotopy-series solutions provides us much larger freedom to choose the auxiliary linear operator L and initial guess: with such kind of guarantee in the frame of the HAM, a nonlinear ODE with variable coefficients can be transferred into a sequence of li”
A general approach to get series solution of non-similarity boundary-layer flows (2009, methodology): “Furthermore, the homotopy analysis method has been applied to solve some non-linear partial differential equations, such as unsteady similarity boundary-layer flows [40], Black–Scholes type equation in finance for American put option [52,53] and interaction of non-linear water wave and exponential s”