chapter  1
12 Pages

Introduction to numerical methods for problems with boundary layers

Note that once we allow the parameter e in ( ) to become small we en­ ter the mathematical realm of singular perturbation problems. The solution of a singularly perturbed problem of the form (1 .1) normally has a smooth and a singular component; its singular component is called a boundary layer function. The boundary layer corresponding to this boundary layer function is the subdo­ main in which the magnitude of the singular component is not negligible. The physical properties associated with a solution containing a boundary layer func­ tion are reflected by the mathematical properties of the solution of a singularly perturbed differential equation. In this book we consider singularly perturbed differential equations with the small parameter e multiplying some or all of the terms involving the highest order derivatives.