Asymptotic Analysis Singularly Perturbed Problem With Singularity

This paper contains two parts to study the asymptotic solution of some kinds of singularly perturbed problems with singularity.In the first part,a numerical integration method is used to solve the singular singularly perturbed second order differential equation with boundary value problem.In the second part,the asymptotic behavior of the problem for the singularly perturbed differential equation with a degenerate equation having multiple root is studied.The first chapter briefly introduces the background and significance of this study,and outline singular perturbation problems and the development of the method of singular perturbation.The second chapter of this article provides a brief overview of the basic knowledge.A numerical integration method for solving singular singularly perturbed second order differential equation with boundary value problem is introduced in chapter three.Some examples are enumerated to demonstrate the applicability of the method.In chapter four to six,we study the asymptotic behavior of the problem for the singularly perturbed nonlinear differential equation with degenerate equation having higher order multiple root.In order to obtain a more precise description of the boundary layer,the modified method of boundary layer function is chosen to construct the boundary layer function possessing the behavior of exponential decay characteristics,and then the asymptotic solution is constructed and used to prove that the formal asymptotic solution is uniformly valid.