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Variational iteration method – some recent results and new interpretations. (English) Zbl 1119.65049
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.

65J15Equations with nonlinear operators (numerical methods)
65H05Single nonlinear equations (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
34L05General spectral theory for OD operators
34A34Nonlinear ODE and systems, general
65K10Optimization techniques (numerical methods)
49J15Optimal control problems with ODE (existence)