Vatiational Iteration Method For Solving The Double Pantograph Delay Differential Equation

Delay Differential Equation, also called Backward Differential Equation, is widely used in various scientific fields. It is also a major subject that all fields are doing research into at present. Delay Differential Equation refers to a differential equation with delayed terms. Nowadays, solving these differential equations is mainly focused on solving the delayed terms approximately, basically following the numerical methods for ordinary differential equations. This thesis is to study the improved variational iteration method for solving double the proportion of delay differential equations, and prove that this method is convergent.The thesis consists of five chapters:Chapter One briefly introduces the background and significance of the research of Delay Differential Equation. First, it gives the general ideas of Delay Differential Equation and later introduces the development and achievement of variational iteration method.Chapter Two first gives the definition and extremum of founctional, on the basis of which the concept and necessary condition of founctional are given. At last, it introduces the direct methods of variational problem.Chapter Three first makes a brief introduction to the basic ideas and simple application of variational iteration method. Then it talks about the convergence rate of the iterative solution and at last the general form of iterative solution.Chapter Four makes a brief introduction to the application of variational iteration method in double pantograph delay differential equation as well as the proof of its convergence.Chapter Five mainly introduces the application of variational iteration method in some other delay differential Equations.