Homotopy analysis method for heat radiation equations

By Saeid Abbasbandy. 2007

275 citations recorded by the source corpus.

Subfields: Computational Mechanics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ef1006e39cb7e866661d1f9e9bc5c0f961c77c62

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In Computational Mechanics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A General Approach to Obtain Series Solutions of Nonlinear Differential Equations (2007, methodology): “The homotopy analysis method has been successfully applied to many nonlinear problems in science and engineering, such as the similarity boundary-layer flows [27, 37‐39], nonlinear heat transfer [40, 33, 35 ], nonlinear evaluation equations [41], nonlinear waves [34], viscous flows of non-Newtonian”
Explicit analytical solutions of the generalized Burger and Burger–Fisher equations by homotopy perturbation method (2009, methodology): “For example, it was applied to the quadratic Ricatti differential equation by Abbasbandy [17], to the axisymmetric flow over a stretching sheet by Ariel et al. [18], to the nonlinear systems of reaction–diffusion equations by Ganji and Sadighi [19], to the Helmholtz equation and fifth-order KdV equa”
A general approach to get series solution of non-similarity boundary-layer flows (2009, methodology): “Based on homotopy, which is a basic concept in topology, a analytic method, namely the homotopy analysis method (HAM) [38–42], is proposed and then widely applied to solve strongly non-linear problems in science, engineering and finance [43–56].”
Notes on the homotopy analysis method: Some definitions and theorems (2009, background): “In most cases, the zeroth-order deformation equation (16) can give satisfied homotopyseries solution, if the auxiliary linear operator L, the auxiliary function Hð~x; tÞ and convergence-control parameter h are properly chosen, as pointed out by Liao [21–23,25,60,26] and others [28–59].”