On The Convergence of the Variational Iteration Method Applied to Variable Coefficient Klein-Gordon Problems

In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has solutions in terms of Airy functions. We prove that the sequence of approximate solutions generated by the variational iteration method for such Klein-Gordon equation converges to Airy functions.