APPLICATION OF VARIATIONAL ITERATION METHOD FOR THE ANALYTICAL SOLUTIONS OF LINEAR AND NON LINEAR DELAY DIFFERENTIAL EQUATIONS USING LAGRANGE MULTIPLIER

The paper employs the variational Iteration Method (VIM), to obtain analytical solution of Linear and Non linear Delay Differential equation (DDE). The method is base on the use of Lagrange multiplier for identification of optimal value of a parameter on a function, the procedure is a powerful tool for solving large amount of problems, using VIM it is possible to find the exact solution of the function. 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. The method is an effective technique for choosing a reasonable initial solution designed in the solving process. Four examples are given to elucidate the method. Comparison is made between collocation splin method based on lagrange interpolation and the present VIM method with exact solution , the solution is calculated in the form of a convergent series with an easy computable component. In conclusion the results show that VIM provide the straight forward and powerful mathematical tool for solving various linear and nonlinear differential equations of the nth order. The method is recommended due to it high accuracy and also can overcome the difficulties arising in the calculation of Adomian’s polynomials, the method does not require small parameters which are needed in perturbation method.