The Theoretical Basis Of Van Dyke Matching Method

In this paper,we mainly discuss the basis theory of Van Dyke Matching Method,which is used to solve second-order linear systemsecond-order quasi-linear systemIn chapter 1,we simply introduce singular perturbation theory of ODE,some methods,and the workhas been down.In chapter 2 and 3,we discuss the above two systems with boundary values.We notonly clarify the difference and relationship between matching method and boundary layer functionmethod,but also prove the existence of the solution of the system and estimate the remainder term.At last,we extend the foregoing problems forward for the readers to think about and work it out.