Fitted Numerical Methods for Singular Perturbation Problems
Subtitle: error estimates in the maximum norm for linear problems in one and two dimensions
Contributors: O'Riordan, E.; Shishkin, G. I.
Edition: Rev. ed.
Publisher: World Scientific
Published: 2012
Place of publication: Singapore
Language: eng
Number of pages: 176
ISBN-13: 9789814390736
Description: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
Table of contents: title: Motivation for the Study of Singular Perturbation Problems; Simple Examples o Singular Perturbation Problems; Numerical Methods for Singular Perturbation Problems; Fitted Operator Methods; Simple Fitted Mesh Methods in One Dimension Fitted Mesh Methods for Reaction-Diffusion Problems; Properties of Upwind Operators on Piecewise Uniform Meshes; Fitted Mesh Methods for Convection-Diffusion Problems; Fitted Element Methods for Convection-Diffusion Problems; Schwarz Iterative Methods in One Dimension; Convection-Diffusion Problems in Two Dimensions; Bounds on Derivatives of Solutions of Convection-Diffusion Problems; Convergence of Fitted Mesh Methods in Two Dimensions; Limitations of Fitted Operators for Parabolic Boundary Layers; Initial and Parabolic Boundary Layers.