Analytical Solution of Time-Fractional Navier-Stokes Equation by Natural Homotopy Perturbation Method

2018 ◽  
Vol 4 (2) ◽  
pp. 123-131 ◽  
Author(s):  
Shehu Maitama
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Stokes Equation ◽  
Homotopy Perturbation Method ◽  
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 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 . 

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

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