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Homotopy Perturbation Method (homotopy + perturbation_method)
Selected AbstractsHe's homotopy perturbation method for solving Korteweg-de Vries Burgers equation with initial conditionNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010Mustafa Inc Abstract In this article, we present the Homotopy Perturbation Method (Shortly HPM) for obtaining the numerical solutions of the Korteweg-de Vries Burgers (KdVB) equation. The series solutions are developed and the reccurance relations are given explicity. The initial approximation can be freely chosen with possibly unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very simple and effective. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] Non-perturbative solution of three-dimensional Navier,Stokes equations for the flow near an infinite rotating diskMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2010Ahmet Y Abstract In this paper, we present Homotopy perturbation method (HPM) and Padé technique, for finding non-perturbative solution of three-dimensional viscous flow near an infinite rotating disk. We compared our solution with the numerical solution (fourth-order Runge,Kutta). The results show that the HPM,Padé technique is an appropriate method in solving the systems of nonlinear equations. The mathematical technique employed in this paper is significant in studying some other problems of engineering. Copyright © 2009 John Wiley & Sons, Ltd. [source] Homotopy perturbation method for numerical solutions of KdV-Burgers' and Lax's seventh-order KdV equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010Ahmet Yildirim Abstract In this article, we applied homotopy perturbation method to obtain the solution of the Korteweg-de Vries Burgers (for short, KdVB) and Lax's seventh-order KdV (for short, LsKdV) equations. The numerical results show that homotopy perturbation method can be readily implemented to this type of nonlinear equations and excellent accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] He's homotopy perturbation method for two-dimensional heat conduction equation: Comparison with finite element methodHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2010M. Jalaal Abstract Heat conduction appears in almost all natural and industrial processes. In the current study, a two-dimensional heat conduction equation with different complex Dirichlet boundary conditions has been studied. An analytical solution for the temperature distribution and gradient is derived using the homotopy perturbation method (HPM). Unlike most of previous studies in the field of analytical solution with homotopy-based methods which investigate the ODEs, we focus on the partial differential equation (PDE). Employing the Taylor series, the gained series has been converted to an exact expression describing the temperature distribution in the computational domain. Problems were also solved numerically employing the finite element method (FEM). Analytical and numerical results were compared with each other and excellent agreement was obtained. The present investigation shows the effectiveness of the HPM for the solution of PDEs and represents an exact solution for a practical problem. The mathematical procedure proves that the present mathematical method is much simpler than other analytical techniques due to using a combination of homotopy analysis and classic perturbation method. The current mathematical solution can be used in further analytical and numerical surveys as well as related natural and industrial applications even with complex boundary conditions as a simple accurate technique. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20292 [source] On the solution of the nonlinear Korteweg,de Vries equation by the homotopy perturbation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009Ahmet Yildirim Abstract In this paper, the homotopy perturbation method is used to implement the nonlinear Korteweg,de Vries equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components. A suitable choice of an initial solution can lead to the needed exact solution by a few iterations. Copyright © 2008 John Wiley & Sons, Ltd. [source] Application of adapted homotopy perturbation method for approximate solution of Henon-Heiles systemNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2010Filiz Ta Abstract We performed adapted homotopy perturbation method on the Henon-Heiles system with the help of the symbolic computation of package Maple 10 (User Manual by Maplesoft. www.maplesoft.com). We obtained a new approximate solution of the Henon-Heiles system. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] Homotopy perturbation method for numerical solutions of KdV-Burgers' and Lax's seventh-order KdV equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010Ahmet Yildirim Abstract In this article, we applied homotopy perturbation method to obtain the solution of the Korteweg-de Vries Burgers (for short, KdVB) and Lax's seventh-order KdV (for short, LsKdV) equations. The numerical results show that homotopy perturbation method can be readily implemented to this type of nonlinear equations and excellent accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] He's homotopy perturbation method for solving Korteweg-de Vries Burgers equation with initial conditionNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010Mustafa Inc Abstract In this article, we present the Homotopy Perturbation Method (Shortly HPM) for obtaining the numerical solutions of the Korteweg-de Vries Burgers (KdVB) equation. The series solutions are developed and the reccurance relations are given explicity. The initial approximation can be freely chosen with possibly unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very simple and effective. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] | |||||||||||||