Study On The Features Of Solutions Of Two Kinds Of Singular Perturbation Systems

This paper mainly studies two kinds of singular perturbation differential systems(singularly perturbed delaying differential systems and singularly perturbed non-delaying differential sys-tems).The existence theorem and convergent proof of solutions are given on the basis of primary studies.In this paper,the following two main problems are being studied:For the boundary value problem of a singularly perturbed delaying differential equations,the core method is dealing with the delayed terms by using the idea of the polynomial expan-sion in the perturbation method.Then,different existence theorems can be given according to the positions of the boundary layers;For those singularly perturbed non-delaying differential systems whose initial value cannot be solved by the traditional perturbation method,a simple and effective iterative method is given by using the iterative idea combining with the charac-teristics of the perturbation method.And then some typical examples are listed to illustrate the utility of the method being used in solving the problems in nonlinear singular perturbed systems.At the same time,the windowing technique is applied to accelerate the convergence of the iterative process and the error estimating formula of the approximate solution after the nth iteration is given as well.These methods can be easily extended to other nonlinear fields and found widely applicable in engineering problems.The first chapter briefly introduces the background of the research and the basic knowl-edge used in this paper,and gives the main results obtained in it.In Chapter 2,the existence of the solution of boundary value problems,one of the singularly perturbed delaying func-tional differential equations,is being studied.In Chapter 3,the initial value of a singular perturbation differential equations is demonstrated.Chapter 4 makes a conclusion for the whole paper and rises the problems for further study.