FITTED NUMERICAL METHODS FOR SINGULAR PERTURBATION PROBLEMS
Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
(Revised Edition)
by J J H Miller (Trinity College, Ireland), E O'Riordan (Dublin City University, Ireland),
&
G I Shishkin (Russian Academy of Sciences, Russia)
Table of Contents (122k)
Preface (157k)
Chapter 1: Motivation for the Study of Singular Perturbation Problems (183k)
About John Miller About Eugene O' Riordan About Grigory Shishkin
Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
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