Numerical and theoretical treatment for solving linear and nonlinear delay differential equations using variational iteration method

Abstract

This article is devoted to use the variational iteration method (VIM) established by J.H. He for solving linear and nonlinear delay differential equations (DDEs). This method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Using VIM, it is possible to find the exact solution or an approximate solution of the proposed problem. This technique provides a sequence of functions which converges to the exact solution of the problem. Convergence analysis is reliable enough to estimate the maximum absolute error of the approximate solution given by VIM. A comparison with the Adomian decomposition method is given.