Convergence Of Variational Iteration Method For Second-Order Delay Defferential Equations

The variational iteration method(VIM) has been successfully used to obtain the analytical solutions or the approximation analytical solutions of many kinds of integral equations, differential equations and integro-differential equations. This is a powerful tool to resolve various types of nonliner problems. The second-order delay differential equations often appear in the dynamical system and control fields etc. Only a very small number of special second-order delay differential equations can receive the expression of the analytical solutions. Therefore, it is very significant to research the numerical method of the approximation analytical solution of these equations.This paper mainly considers the VIM for solving second-order delay dif-ferential equations. In chapter1, we introduce the background of the VIM, second-order delay differential equations and the main work of this paper. In chapter2, the VIM is applied for solving the approximate analytical solution of the general second-order delay differential equations, and we get the convergent results. In chapter3, we use the VIM for solving the approximate solutions of the second-order oscillation delay differential equations, then we receive the sim-ilar convergent results, and some numerical examples show the high accuracy of the method. In chapter4, we modify the iterative method and re-construct the Lagrange multiplier for improving the iteration speed. Then we apply it to solve the approximate analytical solutions of the second-order delay differential equations. Numerical experiments show that this method can effectively improve the speed of iterative.