 
Journal: Nonlinear Science Letters A (ISSN 25199072(Online), ISSN 20762275 (Print)) Vol. 1 No. 1 
The Variational Iteration Method Which Should Be Followed 
JiHuan He^{1}, GuoCheng Wu^{1} , F. Austin^{2} 
1. Donghua University, 1882 Yan’an Xilu Road, Shanghai 200051, China Email: jhhe@dhu.edu.cn 2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China 
Abstract: This paper proposes three standard variational iteration algorithms for solving differential equations, integrodifferential equations, fractional differential equations, fractal differential equations, differentialdifference equations and fractional/fractal differentialdifference equations. The physical interpretations of the fractional calculus and the fractal derivative are given and an application to discrete lattice equations is discussed. The paper then examines the acceleration of some iteration formulae with particular emphasis being placed on the exponential Padé approximant that is suggested for solitary solutions and the sinusoidal Padé approximant that is usually used for periodic and compacton solutions. The paper points out that there may not be any physical meaning to the exact solutions of many nonlinear equations and stresses the importance of searching for approximate solutions that satisfy both the equations and the appropriate initial/boundary conditions. The variational iteration method is particularly suitable for solving this kind of problems. Approximate initial/boundary conditions and point boundary initial/conditions are also discussed, with the variational iteration method being capable of recovering the correct initial/boundary conditions and finding the solutions simultaneously. 
Keywords: Variational iteration method; nonlinear equation; fractional differential equations; fractal differential equation; differentialdifference equation; fractal differentialdifference equation; fractal spacetime; porous flow; Lotka–Volterra equation; predatorprey model; solitary solutions; exponential Padé approximant; sinusoidal Padé approximant; approximate initial/boundary conditions; point boundary /initial conditions. 
Biographical Notes: J. H. He is a Professor at Donghua University. He has published more than 100 articles in ISIlisted journals, the total citation is more than 6,800 and Hindex is 39. He is the editorinchief of International Journal of Nonlinear Sciences and Numerical Simulation. His current research interest mainly covers in nonlinear science, textile engineering, nanotechnology, and biology. http://works.bepress.com/ji_huan_he/ 
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