Application of He's variational iteration method for solution of the family of Kuramoto–Sivashinsky equations

In this paper, a kind of analytical technique for a non-linear problem called the variational iteration method VIM is used to give approximate solutions for the Kuramoto–Sivashinsky equations. The VIM is to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. This method constructs a convergent sequence of functions, which approximates the exact solution of problems. Comparisons of the obtained results with exact solutions reveal that this method is very effective and simple and could be applied for non-linear problems.