New applications of variational iteration method

By Mohamed Aly Mohamed Abdou, Abdel-Maksoud Abdel-Kader Soliman. 2005

370 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d4928acb650ec4219d1f3d1970dba375aa1516f9

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In Mechanics of Materials

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Variational iteration method for solving twelfth-order boundary-value problems using He’s polynomials (2010, methodology): “The variational iteration and homotopy perturbation methods have been applied to a wide class of functional equations; see [1 – 3, 9 – 21, 23 – 41, 45] and the references therein.”
Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations (2011, methodology): “Several techniques including the Adomian decomposition method, the variational iteration method, the weighted finite difference techniques and the Laplace decomposition method have been used to handle advection equations [18-24].”
Modified simple equation method for nonlinear evolution equations (2010, methodology): “This paper outlines the implementation of modified simple equation method (MSEM) for solving evolution equations [1–12] which are very important in applied sciences.”
Application of the Variational Iteration Method for System of Nonlinear Volterra’s Integro-Differential Equations (2009, methodology): “It was successfully applied to autonomous ordinary differential equation [4], to nonlinear partial differential equations with variable coefficients [5], to SchrödingerKDV, generalized KDV and shallow water equations [6], to Burgers' and coupled Burgers' equations [7], to the linear Helmoltz partial”
Variational iteration method for solving two-point boundary value problems (2007, methodology): “It was successfully applied to delay differential equations [5], to Duffing equation with non-linearity of fifth order and mathematical pendulum [7], to Burger’s equation and coupled Burger’s equation [1], to generalized KdV and coupled Schrodinger–KdV [2], to construct solitary solution and compact”
Variational iteration method: New development and applications (2007, methodology): “Wave solutions The variational iteration method is an effective method for searching for various wave solutions including periodic solutions, solitons, compacton solutions without linearization or weak nonlinearity assumptions [16–28].”
Homotopy perturbation transform method for nonlinear equations using He's polynomials (2011, methodology): “Several techniques including the Adomian decomposition method, the variational iteration method, the weighted finite difference techniques and the Laplace decomposition method have been used to handle advection equations [18–24].”
Variational iteration method—Some recent results and new interpretations (2007, positive): “Starting from pioneering ideas going back to Inokuti–Sekine–Mura method [16], the method has matured into a fully fledged theory thanks to the effects of many researchers, notably, Wazwaz [27], Draganescu [6,7], Abdou and Soliman [1–4,23,24], Odibat and Momani [19–22], Bildik [5], Marinca [17], Mogh”
Extended Auxiliary Equation Method and Its Applications to Three Generalized NLS Equations (2014, methodology): “In the past decades, many powerful methods for solving NLPDEs have been developed, such as the inverse scattering method [1], Bäcklund and Darboux transform [2, 3], Hirota’s bilinearmethod [4], Painlevé analysis method [5], variable separationmethod [6–8], tanh-functionmethod [9– 11], variational it”