On the homotopy analysis method for nonlinear problems

By Shijun Liao. Applied Mathematics and Computation, 2004

1,840 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7a1518cabc7795d97aa5aea3e223f687f51d76e4

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 Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate (2006, methodology): “Differentiating the zeroth-order deformation equations (54)–(56) m times with respect to q, then dividing by m!, and finally setting q = 0, we have the mth-order deformation equations (see Liao [28, 29]) L[Fm(z, ξ ) − χm Fm−1(z, ξ )] = Rm( Fm−1, δm−1, z, ξ ), (64)”
Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations (2013, methodology): “We consider the time-fractional damped burger equation Dα t u+uux −uxx +λu = 0 (4)”
Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid (2004, methodology): “The resulting nonlinear, ordinary differential equations are solved analytically using HAM [9]–[ 15 ].”
MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel (2006, methodology): “Analytic solutions are obtained using the homotopy analysis method (HAM) proposed by Liao [36, 37 ].”
A General Approach to Obtain Series Solutions of Nonlinear Differential Equations (2007, methodology): “Furthermore, as proved by Liao [13, 27], the homotopy analysis method logically contains the so-called nonperturbation methods such as Adomian’s decomposition method [4–9], the”
A new branch of solutions of boundary-layer flows over a permeable stretching plate (2007, methodology): “The HAM has been successfully applied to many non-linear problems, such as similarity boundary-layer flows [42–45], non-linear heat transfer [39], non-linear oscillations [32,33], non-linear waves [40], Thomas–Fermi atom model [32], Volterra’s population model [32], high-dimensional Gelfand equation”
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.”
Solution of Delay Differential Equation by Means of Homotopy Analysis Method (2009, neutral): “of differential equations [8–12].”