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De Vries Equation (de + vry_equation)

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Mathematics and Statistics60%

Selected Abstracts

On the solution of the nonlinear Korteweg,de Vries equation by the homotopy perturbation method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009
Ahmet 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]

On the uniform decay for the Korteweg,de Vries equation with weak damping

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2007
C. P. Massarolo
Abstract The aim of this work is to consider the Korteweg,de Vries equation in a finite interval with a very weak localized dissipation namely the H,1 -norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the subject (Q. Appl. Math. 2002; LX(1):111,129; ESAIM Control Optim. Calculus Variations 2005; 11(3):473,486) and gives a satisfactory answer to a problem suggested in (Q. Appl. Math. 2002; LX(1):111,129). Copyright © 2007 John Wiley & Sons, Ltd. [source]

Variational iteration method for solving the space- and time-fractional KdV equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
Shaher Momani
Abstract This paper presents numerical solutions for the space- and time-fractional Korteweg,de Vries equation (KdV for short) using the variational iteration method. The space- and time-fractional derivatives are described in the Caputo sense. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and accurate when applied to space- and time-fractional KdV equations. The method introduces a promising tool for solving many space,time fractional partial differential equations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]