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.


65J15 Numerical solutions to equations with nonlinear operators
65H05 Numerical computation of solutions to single equations
47J25 Iterative procedures involving nonlinear operators
34L05 General spectral theory of ordinary differential operators
34A34 Nonlinear ordinary differential equations and systems
65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
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