An approximate analytical solution of fractional 2D Navier-Stokes equation using homotopy-perturbation method

2015 ◽  
Author(s):  
N. Kumaresan ◽  
Kuru Ratnavelu
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Stokes Equation ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Homotopy Perturbation

Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels

2010 ◽  
Vol 225 (2) ◽  
pp. 347-353 ◽  
Author(s):  
M S Shadloo ◽  
A Kimiaeifar
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Viscoelastic Fluids ◽  
Navier Stokes ◽  
Effective Parameters ◽  
Linear Ordinary Differential Equations ◽  
Homotopy Perturbation ◽  
Magnetohydrodynamic Flows ◽  
Energy Equations

In this article, an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels is presented. A similarity transform reduces the Navier—Stokes and energy equations to a set of non-linear ordinary differential equations that are solved analytically by means of the homotopy perturbation method (HPM). The results obtained in this study are compared with numerical results and previous studies. Close agreement of the two sets of results indicates the accuracy of HPM. An expression that is acceptable for all values of effective parameters is obtained by HPM. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on HPM.

scholarly journals An Approximate Analytical Solution Of Nonlinear Equations In N-Aminopiperidine Synthesis: New Approach Of Homotopy Perturbation Method)

2021 ◽  
Vol 12 (1S) ◽  
pp. 595-605
Author(s):  
R. Joy Salomi, Et. al.
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Rate Equations ◽  
Simple Analytical Expression ◽  
New Approach ◽  
Homotopy Perturbation ◽  
Numerical Result

the synthesis of N-aminopiperidine (NAPP) using hydroxylamine-O-sulfonic acid (HOSA) is based on system of nonlinear rate equations. The new approach to homotopy perturbation method is applied to solve the nonlinear equations. A simple analytical expression for concentrations of hydroxylamine-O-sulfonique acid (HOSA), piperidine (PP), N-aminopiperidine (NAPP), sodium hydroxide (NaOH) and diazene (N2H2) along with NAPP yield is obtained and is compared with numerical result. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. The obtained analytical result of NAPP yield is compared with the experimental results. The influence of reagents ratio p and rate constants ratio r on yield has been discussed.

scholarly journals Splitting Decomposition Homotopy Perturbation Method To Solve One -Dimensional Navier -Stokes Equation

2017 ◽  
Vol 13 (2) ◽  
pp. 7123-7134 ◽  
Author(s):  
A. S. J Al-Saif ◽  
Takia Ahmed J Al-Griffi
Keyword(s):  
Exact Solution ◽  
Stokes Equation ◽  
Homotopy Perturbation Method ◽  
Differential Operators ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Splitting Time

We have proposed in this  research a new scheme to find analytical  approximating solutions for Navier-Stokes equation  of  one  dimension. The  new  methodology depends on combining  Adomian  decomposition  and Homotopy perturbation methods  with the splitting time scheme for differential operators . The new methodology is applied on two problems of  the test: The first has an exact solution  while  the other one has no  exact solution. The numerical results we  obtained  from solutions of two problems, have good convergent  and high  accuracy   in comparison with the two traditional Adomian  decomposition  and Homotopy  perturbationmethods . 

scholarly journals Approximate analytical solution for Phi-four equation with he’s fractal derivative

2021 ◽  
pp. 127-127
Author(s):  
Shuxian Deng ◽  
Xinxin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Integral Transform ◽  
Approximate Analytical Solution ◽  
Homotopy Perturbation ◽  
Fractal Derivative ◽  
Fractal Differential Equations ◽  
First Time

This paper, for the first time ever, proposes a Laplace-like integral transform, which is called as He-Laplace transform, its basic properties are elucidated. The homotopy perturbation method coupled with this new transform becomes much effective in solving fractal differential equations. Phi-four equation with He?s derivative is used as an example to reveal the main merits of the present technology.

scholarly journals Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
European Option ◽  
European Option Pricing ◽  
Homotopy Perturbation ◽  
Black Scholes ◽  
Sumudu Transform

The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.

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