Convergence Of Pantograph Equations

During the past decades,lots of important theories and numerical results have been obtained for ordinary differential equations and partial differential equations.Similarly,the research of pantograph equations also have the very important actual value.In this work ,we mainly applies one specialθ-method and the variational iteration method to consider the convergence of pantograph equations and obtains proof of the convergence.The work consists of three parts as follows:Firstly,we briefly reviews the origin and the research development of pantograph equations,simultaneously shows the good and bad points of pantograph equations research.Next,we introduces partial ordering concept in the algebra,constructs on specialθ-method to solve the pantograph equations,obtains the very good convergence results.Finally ,we introduces iteration scheme of variational iteration method and uses variational iteration method to solve pantograph equations,may obtain the convergence results for first-order pantograph equations as well as the mult-order pantograph equations.