scholarly journals A COMPARISON OF THE ADOMIAN AND HOMOTOPY PERTURBATION METHODS IN SOLVING THE PROBLEM OF SQUEEZING FLOW BETWEEN TWO CIRCULAR PLATES

2010 ◽  
Vol 15 (4) ◽  
pp. 491-504 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Tahira Haroon ◽  
Saira Bhatti ◽  
Ali R. Ansari
Keyword(s):  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Computational Effort ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier‐Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench‐marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

scholarly journals Analytic Comparison of MHD Squeezing Flow in Porous Medium with Slip Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Transform Method ◽  
Slip Boundary ◽  
Adomian Decomposition

The aim of this paper is to compare the efficiency of various techniques for squeezing flow of an incompressible viscous fluid in a porous medium under the influence of a uniform magnetic field squeezed between two large parallel plates having slip boundary. Fourth-order nonlinear ordinary differential equation is obtained by transforming the Navier-Stokes equations. Resulting boundary value problem is solved using Differential Transform Method (DTM), Daftardar Jafari Method (DJM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Optimal Homotopy Asymptotic Method (OHAM). The problem is also solved numerically using Mathematica solver NDSolve. The residuals of the problem are used to compare and analyze the efficiency and consistency of the abovementioned schemes.

scholarly journals Fast solvers for finite difference approximations for the stokes and navier-stokes equations

1996 ◽  
Vol 38 (2) ◽  
pp. 274-290 ◽  
Author(s):  
Dongho Shin ◽  
John C. Strikwerda
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Linear Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Fast Solvers ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Grid Points ◽  
First Time

AbstractWe consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.

scholarly journals Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Norhasimah Mahiddin ◽  
S. A. Hashim Ali
Keyword(s):  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Slight Variation ◽  
Tumour Invasion ◽  
Invasion And Metastasis ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability

2010 ◽  
Vol 65 (12) ◽  
pp. 1033-1038 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yıldırım ◽  
Sefa Anıl Sezer
Keyword(s):  
Series Solution ◽  
Analytical Approach ◽  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Rectangular Channel ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Remarkable Improvement ◽  
Homotopy Perturbation ◽  
Expanding Or Contracting Walls

In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.

scholarly journals The Analysis of Fractional-Order Navier-Stokes Model Arising in the Unsteady Flow of a Viscous Fluid via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pongsakorn Sunthrayuth ◽  
Rasool Shah ◽  
A. M. Zidan ◽  
Shahbaz Khan ◽  
Jeevan Kafle
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Navier Stokes ◽  
Power Series Method ◽  
Navier Stokes Equations ◽  
Residual Power Series ◽  
Residual Power

This paper presents a new method that is constructed by combining the Shehu transform and the residual power series method. Precisely, we provide the application of the proposed technique to investigate fractional-order linear and nonlinear problems. Then, we implemented this new technique to obtain the result of fractional-order Navier-Stokes equations. Finally, we provide three-dimensional figures to help the effect of fractional derivatives on the actions of the achieved profile results on the proposed models.

NEW ANALYTICAL SOLUTION OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 23 (26) ◽  
pp. 3147-3155 ◽  
Author(s):  
MOHAMMAD MEHDI RASHIDI ◽  
GANJI DOMAIRRY
Keyword(s):  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Differential Transform ◽  
Conditions At Infinity

The purpose of this study is to implement a new analytical method (the DTM-Padé technique, which is a combination of the differential transform method (DTM) and the Padé approximation) for solving Navier–Stokes equations. In this letter, we will consider the DTM, the homotopy perturbation method (HPM) and the Padé approximant for finding analytical solutions of the three-dimensional viscous flow near an infinite rotating disk. The solutions are compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that the application of the Padé approximants in the DTM and HPM is an appropriate method in solving the Navier–Stokes equations with the boundary conditions at infinity. On the other hand, the convergence of the obtained series from DTM-Padé is greater than HPM-Padé.

First Order Reliability Analogies of Nonlinear Bending Moments in Ships

2013 ◽  
Author(s):  
Jan Oberhagemann ◽  
Vladimir Shigunov ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Bending Moments ◽  
Sea State ◽  
Nonlinear Bending ◽  
Navier Stokes Equations ◽  
Hull Girder ◽  
First Order

Hydroelasticity codes based on the solution of the Navier-Stokes equations are beneficial for extreme value predictions of hull girder loads. Since direct long-term analyses using these numerical methods are prohibitive due to excessively large required computation times, strategies are sought to reduce the computational effort. An extrapolation approach allows reducing the required simulation duration significantly. Application to hogging bending moments of flexible containerships agrees with Monte-Carlo simulations in random sea state realisations.

scholarly journals An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hajira ◽  
Hassan Khan ◽  
Adnan Khan ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Stokes Equations ◽  
Approximate Analytical Solution ◽  
Nonlinear Problems ◽  
Current Method ◽  
Navier Stokes ◽  
Hybrid Technique ◽  
Navier Stokes Equations ◽  
Research And Innovation ◽  
Strong Relation

Abstract In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.

Sign in / Sign up

Export Citation Format

Share Document