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Zbl 1119.65049
He, Ji-Huan
Variational iteration method -- some recent results and new interpretations. (English)
[J] J. Comput. Appl. Math. 207, No. 1, 3-17 (2007). ISSN 0377-0427

Summary: 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.

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
65H05 Single nonlinear equations (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)
34L05 General spectral theory for ODE
34A34 Nonlinear ODE and systems, general
65K10 Optimization techniques (numerical methods)
49J15 Optimal control problems with ODE (existence)

Keywords: variational iteration method; nonlinear equations; numerical examples; Lagrange multiplier; restricted variation, correction functional; nonlinear oscillators

Cited in: Zbl 1244.65104 Zbl 1190.65197 Zbl 1176.65059

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Zentralblatt MATH Berlin [Germany]