The Step-Type Contrast Structure Of A Class Of Singularly Perturbed Differential-Difference Equation

Recently,a great deal of scholars have researched different types of singularly perturbed difference differential equations and apply in the fields of science and engineering.With the complexity of the original and degenerate problems,there are some problems to be solved,such as the solution of step-type contrast structure with multiple internal transfer layers.In this thesis,we investigate the step-type contrast structure of a class of singularly perturbed difference differential equation.We employ the classical singular perturbation theory and method to solve this problem,obtaining its solution with the stepped step-type contrast structure.This thesis consists of three chapters,and the specific contents are arranged as follows.The first chapter reviews the development of singular perturbation theory,briefly introduces the origin and research progress of delay differential equations and the steptype contrast structure,lists the research results of singular perturbation difference differential equations,and briefly describes the basic theorems required in this thesis.Finally,this chapter shows the main content and innovation of this thesis.In Chapter 2,we study the step-type contrast structure of a class of second-order semilinear singularly perturbed difference differential equation.Using the "step-bystep method",the original problem is divided into three pure boundary layer problems:left,middle and right.The asymptotic expressions of each sub-problem are constructed according to the boundary layer function method.Respectively,we smoothly seam the asymptotic solution in t=? and t=t*,proving the existence and uniform validity of the solution on[0,T].Finally,a numerical example is given to verify the feasibility of the algorithm for constructing asymptotic solutions in this chapter.The third chapter is the summary,deficiency and prospect of this thesis.