A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs

2019 ◽  
Vol 42 (18) ◽  
pp. 7222-7232 ◽  
Author(s):  
Zaid Odibat ◽  
Dumitru Baleanu
Keyword(s):  
Homotopy Analysis Method ◽  
Linear Time ◽  
Analysis Method ◽  
Parabolic Pdes ◽  
Non Linear ◽  
Homotopy Analysis

scholarly journals Two Species Commensalism Model with Harvesting by Homotopy Analysis Method

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3584-3588
Keyword(s):  
Linear System ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analytical Study ◽  
Analysis Method ◽  
Linear Ordinary Differential Equations ◽  
Commensal Species ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Non Linear System

In the present investigation a two species commensalism model was taken up for detailed analytical study in which commensal species was harvested at a rate proportional to its strength. The system under investigation was represented by a coupled non linear ordinary differential equations. The series solution of the non-linear system was approximated by Homotopy Analysis Method.

APPLICATION OF THE NEW SPECTRAL HOMOTOPY ANALYSIS METHOD (SHAM) IN THE NON-LINEAR HEAT CONDUCTION AND CONVECTIVE FIN PROBLEM WITH VARIABLE THERMAL CONDUCTIVITY

2012 ◽  
Vol 09 (03) ◽  
pp. 1250039 ◽  
Author(s):  
S. S. MOTSA
Keyword(s):  
Thermal Conductivity ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Linear Heat ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Convective Fin ◽  
Spectral Homotopy Analysis Method

In this work, we demonstrate the efficiency of the newly developed spectral homotopy analysis method (SHAM) in solving non-linear heat transfer equations. We demonstrate the applicability of the method by solving the problem of steady conduction in a slab and the convective fin equation with variable thermal conductivity. New closed form explicit analytic solutions of the governing non-linear equations are obtained and compared with the SHAM results and numerical solutions. The results reveal that the new SHAM approach is very accurate and efficient and converges much faster than the standard homotopy analysis method.

The electrical magnetohydrodynamic (MHD) and shape factor impacts in a mixture fluid suspended by hybrid nanoparticles between non-parallel plates

2021 ◽  
pp. 095440892110579
Author(s):  
Abdelkader Khentout ◽  
Mohamed Kezzar ◽  
Mohamed R. Sari ◽  
Tabet Ismail ◽  
Mustapha S. Tich Tich ◽  
...  
Keyword(s):  
Homotopy Analysis Method ◽  
Fluid Velocity ◽  
Hybrid Nanoparticles ◽  
Graphical Form ◽  
Hybrid Nanofluid ◽  
Parallel Plates ◽  
Analysis Method ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Shape Of Nanoparticles

Abstract In this research work, we introduce the influences of the shape of nanoparticles and joule heating in the hydromagnetic flow of hybrid nanofluids between non-parallel plates. A mixture base fluid (H2O (50%)-C2H6O2 (50%)), a hybrid nanofluid containing hybrid nanoparticles (graphene oxide-molybdenum disulfide, GO-MoS2) as nanoparticles, is considered. The non-linear governing equations are reduced into ordinary-differential equations (ODEs) by similarity transformations. The non-linear ordinary-differential equation (ODE) is solved numerically utilizing 4th–5th order Runge-Kutta-Fehlberg (RKF-45) with a shooting method and analytically using the homotopy analysis method (HAM). The effect of the rarefaction parameter, Reynolds number, channel angle, Hartmann number, electric field parameter, and the shape of nanoparticles on fluid velocity and skin friction are discussed and presented in a graphical form. Also, the theoretical results and the effectiveness of the homotopy analysis method (HAM) are confirmed by numerical tests and presented graphically coupled with detailed discussions.

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Linear Differential Equations ◽  
Analysis Method ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

AbstractThe similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].

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