The variational iteration method (VIM) has been applied to solve many functional equations, so far. In this paper the problem of conversion of three radioactive materials has been studied. By mathematical modeling of the problem a system of ordinary differential equations has been derived. The variational iteration method is applied to obtain exact solution of this system of ordinary differential equations.

In [1], introduce a modified variational iteration method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational iteration method (VIM) and MVIM (introduced in [1]) to obtain exact solution to Fisher’s equation. It is shown in this paper the application of VIM to Fisher’s equation leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions. Therefore, we use MVIM for Fisher’s equation to overcome these disadvantages.

In this paper, the variational iteration method is proposed to solve the Nagumo telegraph equation as boundary value problems over the finite spatial interval x Î [0, L], and finite time t Î [0, t*]. Approximate solution is obtained for some special cases, so that denotes the validity of the variational iteration method. Also, this approximate solution is used to discuss the qualitative characteristics of the solution for specific initial data considered.

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results reveal that VIM is very effective and simple.

In this paper, the tenth-order linear special case boundary value problems are solved using the variational iteration method. The algorithm approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method is simple and valid.

The variational iteration method (VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.