Variational iteration method for autonomous ordinary differential systems

In this paper, a new iteration technique is proposed to solve autonomous ordinary differential systems. In this method, general Lagrange multipliers are introduced to construct correction functionals for the systems. The multipliers in the functionals can be identified by the variational theory. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the boundary/initial conditions. Some examples are given. The results reveal that the method is very effective and convenient.