Variational iteration method—Some recent results and new interpretations

By Ji-Huan He. Journal of Computational and Applied Mathematics, 2007

1,071 citations recorded by the source corpus.

This paper is an elementary introduction to the concepts of variational iteration method. First, the main concepts in variational iteration method, such as general Lagrange multiplier, restricted variation, correction functional, are explained heuristically. Subsequently, the solution procedure is systematically addressed, in particular, for nonlinear oscillators. Particular attention is paid throughout the paper to give an intuitive grasp for the method. The main motivation is to put things together in a convenient form for later reference and systematic use.

Subfields: Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/387d8fc8fca7782ec62adbacd815851e0d68af55

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Citations in the corpus

A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, positive): “The variational iteration method [47–51] has been shown to solve a large class of nonlinear differential problems effectively, easily, and accurately with the approximations converging rapidly to accurate solutions.”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, methodology): “124 The VIM is useful to obtain exact and approximate solutions of linear and nonlinear differen125 tial equations [35, 57, 62, 99, 104, 117, 122, 136, 139, 153, 167, 177, 179, 184, 191, 202, 206].”
AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING (2008, methodology): “In this section, we will introduce some fascinating nano-phenomena using simple physics principles, mainly including the following catalogs: (1) Electrospun Nanofibers; (2) Spider-spinning; (3) Bubbleelectrospinning; (4) Jet-vortex Spinning and Cyclone Model; (5) Two-phase Flow of Yarn Motion in Hig”
Variational iteration method: New development and applications (2007, background): “[9], for a relatively comprehensive survey on the method and its applications, the reader is referred to a review article [5] or a monograph [8].”
The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators (2019, background): “This criterion can be understood by a pendulum-like oscillator u00 1⁄4 fðuÞ u u (3)”
Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials (2008, methodology): “The principles of variational iteration method and its applicability for various kinds of differential equations are given in [16-21].”
An approximation to the solution of telegraph equation by variational iteration method (2009, methodology): “The results of applying VIM are exactly the same as these of Adomian decomposition method [5].”
A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials (2012, methodology): “The method was first initiated by [6], and it was successfully used by various researchers to investigate the linear and nonlinear problems [6, 10].”