Improvement of Heʹs variational iteration method for solving systems of differential equations

In recent years a lot of attention from researchers has been attracted to the various aspects of the well known Heʹs variational iteration method. This method is a very powerful method for solving a large amount of problems. It provides a sequence which converges to the solution of the problem without discretization of the variables. In this work an idea is proposed that accelerates the convergence of the sequences which result from the variational iteration method for solving systems of differential equations. Illustrative examples are presented to show the validity of the new method.