ASSESSMENT OF HOMOTOPY-PERTURBATION AND PERTURBATION METHODS IN HEAT RADIATION EQUATIONS

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Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations (2006, methodology): “HPM was successfully applied to nonlinear oscillators with discontinuities [19], boundary value problems [23], heat radiation equations [24], generalized Hirota-Satsuma coupled KdV equation [25], Helmholtz Equation and Fifth-order KdV Equation [33].”
A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity (2011, background): “A number of recent papers [6–16] have used the homotopy methods to solve nonlinear problems in dynamics, fluid flow and heat transfer.”
Application of Variational Iteration and Homotopy-Perturbation Methods to Nonlinear Heat Transfer Equations with Variable Coefficients (2007, methodology): “One of the recently presented researches is on using the HPM in heat transfer [21, 22].”
Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method (2009, methodology): “In addition, in recent years, scientists have presented some new methods for solving nonlinear partial differential equations; for instance, Bäcklund transformation method [3], Lie groupmethod [4], Adomian’s decomposition method [5], inverse scattering method [6], Hirota’s bilinear method [7], homot”