Singularly Perturbed Boundary Value Problems Via Methods Of Matched Asymptotic Expansions And Composite Expansions

In this dissertation, several types of singularly perturbed boundary value problems are studied using perturbation methods including the method of matched asymptotic expansions and the method of composite expansions.The article consists of three parts. The first chapter provides a brief introduction to be historical development and some application background of singular perturbation, and then presents some preliminary concept and results which will be required later.In the second chapter we study singularly perturbed boundary value problems by the method of matched asymptotic expansions. In section 1, some second order semi linear boundary value problems with two boundary layer phenomena are considered using Prandtl’s matching principle. In section 2, a second order linear boundary value problem with turning points are considered using Van Dyke’s matching principle. In section 3, a second order linear boundary value problem is considered using the immediate variable matching principle.In the third chapter we study singularly perturbed boundary value problems by the method of composite expansions. In section 1, some semi linear boundary valueproblems with nonmonotone transition layer properties are studied. In section 2, a boundary value problem for second order elliptic equations are studied. In section 3,boundary value problems for a class of semi linear second order elliptic equations are studied.