Variational iteration method: Green’s functions and fixed point iterations perspective

The aim of this article is to demonstrate that the variational iteration method “VIM” is in many instances a version of fixed point iteration methods such as Picard’s scheme. In a wide range of problems, the correction functional resulting from the VIM can be interpreted and/or formulated from well-known fixed point strategies using Green’s functions. A number of examples are included to assert the validity of our claim. The test problems include first and higher order initial value problems.