A theoretical model of an electrocatalytic processes taking place at conducting polymer modified electrodes is discussed. In this model the diffusion of solution species, charge carriers and chemical reaction within the film are taken into account. The model involves the system of non-linear non-steady-state reaction diffusion equations. Analytical expressions pertaining to the concentrations a...

This article describes the effect of thermal radiation on the thin film nanofluid flow of a Williamson fluid over an unsteady stretching surface with variable fluid properties. The basic governing equations of continuity, momentum, energy, and concentration are incorporated. The effect of thermal radiation and viscous dissipation terms are included in the energy equation. The energy and concent...

This paper presents the solution of the nonlinear equation that governs the flow of a viscous, incompressible fluid between two converging-diverging rigid walls using an improved homotopy analysis method. The results obtained by this new technique show that the improved homotopy analysis method converges much faster than both the homotopy analysis method and the optimal homotopy asymptotic meth...

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable co...

SONG, H. and TAO, L., 2007. Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. Journal of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), pg – pg. Gold Coast, Australia, ISBN 1-891276-54-9 In this paper, the 1D unsteady, nonlinear groundwater flow through porous media, corresponding to flood in an aquifer between two reservoirs, ...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.

in this paper, the convergence of zakharov-kuznetsov (zk) equation by homo- topy analysis method (ham) is investigated. a theorem is proved to guarantee the conver- gence of ham and to nd the series solution of this equation via a reliable algorithm.

Partial differential equations are known to be increasingly important in today’s research, and their solutions paramount for tackling numerous real-life applications. This article extended the analytical scheme of homotopy analysis method (HAM) develop an approximate solution Fuzzy Differential Equations (FPDEs). The used its powerful tools, auxiliary function convergence-control parameter, opt...

The investigation is to explore the transportation of a viscoelastic fluid with fractional Burgers’ model by peristalsis through a channel under the influence of wall slip condition. This analysis has been carried out under the assumption of long wavelength and low Reynolds number. An approximate analytical solution of the problem is obtained by using Homotopy Analysis method (HAM). It is assum...

The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is tak...