Vatiational Iteration Method & Its Application

It is well known that nonlinear problems are very important in a variety of scien-tific fields, exact or analytic solution of nonlinear equations plays an important role in theory of the mathematical physics. The variational iteration method is successfully applied to nonlinear equations.The motivation of this paper is to extend the modified variational iteration method for solving three different types of nonlinear equations namely, coupled Bur-ger's equation, Klein-Gordon equation and a kind of hyperbolic partial differential equation.The content of this paper is mainly divided into four parts.In the part of introduction, we briefly introduce nonlinear equations and its tradi-tional numerical methods , then we briefly introduce the characteristic, service condi-tion and the development of various numerical methods. At last, we introduce the variational iteration method and its applications.In the second part, we introduce some basic theory of variation, for example, definitions, lemmas, theorems, the direct methods of variation and some important conclusions.In the third part, we first introduce the basic ideas of variational iteration method, then we introduce the formation of variational iteration method and its simple applica-tions, At last, we introduce the modified variational iteration method.In the fourth part of this paper, we give some applications of the modified varia-tional iteration method.