THE INFLUENCE OF A MAGNETIC FIELD ON A LAMINAR VISCOUS FLOW IN A SEMI-POROUS CHANNEL

2010 ◽  
Vol 24 (04) ◽  
pp. 497-513
Author(s):  
A. A. RANJBAR ◽  
G. DOMAIRRY ◽  
M. S. JAVADEIN
Keyword(s):  
Magnetic Field ◽  
Homotopy Perturbation Method ◽  
Viscous Incompressible Fluid ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Two Dimensional ◽  
System Of Differential Equations ◽  
Homotopy Perturbation

In this article, the steady two-dimensional laminar flow of a viscous incompressible fluid in a semi-porous channel in the presence of a transverse magnetic field is considered. The homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of the system of differential equations governing on the problem. Velocity profiles, streamlines, and the other parameters of flow are determined. Comparisons are made between the numerical method (NM) and the results of our methods. The results reveal that these methods are very effective, simple, and can be applied to other nonlinear problems.

The Variational Iteration Method and the Variational Homotopy Perturbation Method for Solving the KdV-Burgers Equation and the Sharma-Tasso-Olver Equation

2010 ◽  
Vol 65 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Hanan M. Abdel Rahman
Keyword(s):  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Alternative Methods ◽  
Variational Iteration ◽  
Homotopy Perturbation

AbstractIn this article, two powerful analytical methods called the variational iteration method (VIM) and the variational homotopy perturbation method (VHPM) are introduced to obtain the exact and the numerical solutions of the (2+1)-dimensional Korteweg-de Vries-Burgers (KdVB) equation and the (1+1)-dimensional Sharma-Tasso-Olver equation. The main objective of the present article is to propose alternative methods of solutions, which avoid linearization and physical unrealistic assumptions. The results show that these methods are very efficient, convenient and can be applied to a large class of nonlinear problems.

scholarly journals An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
F. A. Hendi ◽  
M. M. Al-Qarni
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
New Form ◽  
New Formula

We propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variational accelerated homotopy perturbation method (VAHPM). This approach is based on the form of He’s polynomials and on a new form of He’s polynomials. We discuss the convergence of the technique. Some numerical examples are introduced to verify the efficiency of this technique.

scholarly journals Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Saeed Dinarvand ◽  
Abed Moradi
Keyword(s):  
Shooting Method ◽  
Homotopy Perturbation Method ◽  
Viscous Incompressible Fluid ◽  
Axisymmetric Flow ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Two Dimensional Flow ◽  
Squeeze Number ◽  
Flow Case

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). Graphical results are presented to investigate the influence of the squeeze number on the velocity, skin friction, and pressure gradient. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.

NUMERICAL SOLUTIONS FOR THE NONLINEAR FORNBERG–WHITHAM EQUATION BY HE'S METHODS

2011 ◽  
Vol 25 (32) ◽  
pp. 4721-4732 ◽  
Author(s):  
FAYÇAL ABIDI ◽  
KHALED OMRANI
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Difficult Problem ◽  
Variational Theory ◽  
Science And Engineering ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Whitham Equation

In this paper, variational iteration method (VIM) and homotopy-perturbation method (HPM) are implemented for solving analytically the nonlinear Fornberg–Whitham (FW) equation. VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory HPM converts a difficult problem into simple one, which can be easily handled. Furthermore, the solutions obtained are compared with the corresponding exact solution to show the applicability accuracy and efficiency of the present methods in solving a large class of linear and nonlinear problems arising in different fields of science and engineering.

scholarly journals A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1735
Author(s):  
Shuang-Shuang Zhou ◽  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
S. Saleem ◽  
Kamsing Nonlaopon
Keyword(s):  
Homotopy Perturbation Method ◽  
Graphical Representation ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Computational Techniques ◽  
System Of Nonlinear Equations ◽  
Gas Dynamics Equations ◽  
Homotopy Perturbation ◽  
Fractional System ◽  
Modified Forms

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

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