Introduction to numerical methods for problems with boundary layers
Note that once we allow the parameter e in (l.la ) 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.