FITTED NUMERICAL METHODS FOR SINGULAR PERTURBATION PROBLEMS: ERROR ESTIMATES IN THE MAXIMUM NORM FOR LINEAR PROBLEMS IN ONE AND TWO DIMENSIONS (REVISED EDITION) - Hardcover

Miller, John J H; O'Riordan, Eugene; Shishkin, G I

Hardcover

ISBN 10: 9814390739 ISBN 13: 9789814390736

Publisher: World Scientific Publishing Company, 2012

Synopsis

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.

About this title

About the Author:

John Miller graduated from Trinity College, Dublin, and took his PhD degree in numerical analysis at the Massachusetts Institute of Technology. From 1970 to 2000, he has taught in the Mathematics Department, Trinity College. He is now at the Institute for Numerical Computation and Analysis, Dublin. His research interests include the mathematical modelling of devices for converting ocean wave energy into electric power.

Eugene O' Riordan graduated from University College Dublin in 1977 and received his PhD in 1982 from Trinity College, Dublin. He is currently teaching in the School of Mathematical Sciences, Dublin City University. His research interests include singular perturbation problems, numerical analysis and layer adapted meshes.

Grigory Shishkin graduated in 1961 from the Leningrad Technological Institute as an inorganic chemist. In 1967, he graduated in mathematics from the Ural State University. He obtained his first doctoral thesis in 1974 and his second doctoral thesis in 1990. He is now a leading scientist in the department of mathematical physics in the Institute of Mathematics and Mechanics, Ekaterinburg, Russia. He became involved in singular perturbation problems due to the influence of his scientific mentor A M Il'in.

About this edition

• Publisher: World Scientific Publishing Company
• Publication date: 2012
• ISBN 10: 9814390739
• ISBN 13: 9789814390736
• Binding: Hardcover
• Number of pages: 192