Variational iteration method for solving Burger's and coupled Burger's equations
M.A. Abdou,A.A. Soliman +1 more
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TLDR
In this article, He's variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials, and the solutions of Burger's equation and coupled Burger's equations are exactly obtained.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2005-09-15 and is currently open access. It has received 485 citations till now. The article focuses on the topics: Adomian decomposition method & Partial differential equation.read more
Citations
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Homotopy perturbation method for solving boundary value problems
TL;DR: Wazwaz et al. as mentioned in this paper applied homotopy perturbation method to nonlinear boundary value problems and compared the result obtained by the present method with that obtained by Adomian method.
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Variational iteration method-Some recent results and new interpretations
TL;DR: The main concepts in variational iteration method, such as general Lagrange multiplier, restricted variation, correction functional, are explained heuristically and the solution procedure is systematically addressed, in particular, for nonlinear oscillators.
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Variational iteration method: New development and applications
Ji-Huan He,Xu-Hong Wu +1 more
TL;DR: The basic conceptual framework of variational iteration technique with application to nonlinear problems is outlined and a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested.
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New applications of variational iteration method
M.A. Abdou,A.A. Soliman +1 more
TL;DR: In this article, He's variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled Schrodinger-KdV, generalized KdV and shallow water equations.
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Fractional variational iteration method and its application
Guo-Cheng Wu,Eric Wai Ming Lee +1 more
TL;DR: In this paper, a fractional variational iteration method with modified Riemann Liouville derivative is proposed to solve the fractional differential equations more efficiently, which avoids the term of fractional derivative and handles them as restricted variation.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Journal ArticleDOI
Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
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Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.
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Variational iteration method – a kind of non-linear analytical technique: some examples
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.