Numerical Analysis of Singularly Perturbed Boundary Value Problems.

      Аннотация: In general, any differential equation in which the highest order derivative is multiplied by a small positive parameter is called Singular Perturbation Problem. When we apply the existing standard numerical methods to these singular perturbation problems, we get oscillatory/ unsatisfactorily results. As a result of this, finding solutions of singularly perturbed boundary value problems has become most interesting and challenging task. Thus it is of considerable scientific interest to the researchers to develop simple and efficient computational methods for singularly perturbed two point boundary value problems. In this book, we have proposed and illustrated some simple and efficient numerical techniques for finding the solution of a singularly perturbed two point boundary value problems. This work consists of eight chapters. Chapter 1 deals with definition and survey on singular perturbation problems. Chapters 2 and 3 deals with Fitted methods. In Chapters 4 and 5 we discuss the special methods. Chapter 6 deals with an asymptotic technique. Chapter 7 deals with numerical integration method. Final chapter 8 deals with general conclusion and further scope of research.

Ключевые слова: Boundary Layer, fitting factor, Singular perturbation problems