Analytic solution of singular Emden-Fowler-type equations by Green’s function and homotopy analysis method

2019 ◽  
Vol 134 (11) ◽  
Author(s):  
Randhir Singh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Analysis Method ◽  
Homotopy Analysis

scholarly journals A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation

2014 ◽  
Vol 7 (4) ◽  
pp. 826-831
Author(s):  
Vahid Barati ◽  
Mojtaba Nazari ◽  
Vincent Daniel David ◽  
Zainal Abdul Aziz
Keyword(s):  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Kdv Equation ◽  
Analysis Method ◽  
Homotopy Analysis

Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer Over a Stretching Flat Surface by Homotopy Analysis Method

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Ahmer Mehmood ◽  
Asif Ali
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Porous Plate ◽  
Three Dimensional ◽  
Parallel Plates ◽  
Analysis Method ◽  
Electrically Conducting ◽  
Homotopy Analysis

In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

scholarly journals Analytic Solution of Multipantograph Equation

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Fadi Awawdeh ◽  
Ahmad Adawi ◽  
Safwan Al-Shara'
Keyword(s):  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Convergent Series ◽  
Analysis Method ◽  
Analytical Results ◽  
Homotopy Analysis

We apply the homotopy analysis method (HAM) for solving the multipantograph equation. The analytical results have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method. Comparisons are made to confirm the reliability of the homotopy analysis method.

A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate

1999 ◽  
Vol 385 ◽  
pp. 101-128 ◽  
Author(s):  
SHI-JUN LIAO
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Two Dimensional ◽  
Analysis Method ◽  
Numerical Result ◽  
Homotopy Analysis ◽  
Potential Possibility ◽  
Valid Solution

We apply a new kind of analytic technique, namely the homotopy analysis method (HAM), to give an explicit, totally analytic, uniformly valid solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f‴(η)+αf(η)f″(η)+β[1−f′2(η)]=0 under the boundary conditions f(0)=f′(0)=0, f′(+∞)=1. This analytic solution is uniformly valid in the whole region 0[les ]η<+∞. For Blasius' (1908) flow (α=1/2, β=0), this solution converges to Howarth's (1938) numerical result and gives a purely analytic value f″(0)=0.332057. For the Falkner–Skan (1931) flow (α=1), it gives the same family of solutions as Hartree's (1937) numerical results and a related analytic formula for f″(0) when 2[ges ]β[ges ]0. Also, this analytic solution proves that when −0.1988[les ]β0 Hartree's (1937) family of solutions indeed possess the property that f′→1 exponentially as η→+∞. This verifies the validity of the homotopy analysis method and shows the potential possibility of applying it to some unsolved viscous flow problems in fluid mechanics.

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