Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)
eBook - PDF

Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)

Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions

  1. 192 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)

Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions

About this book

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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Yes, you can access Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) by John J H Miller, Eugene O'riordan, G I Shishkin in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Contents
  2. Preface
  3. Notation, Terminology and Acknowledgments
  4. 1. Motivation for the Study of Singular Perturbation Problems
  5. 2. Simple Examples of Singular Perturbation Problems
  6. 3. Numerical Methods for Singular Perturbation Problems
  7. 4. Simple Fitted Operator Methods in One Dimension
  8. 5. Simple Fitted Mesh Methods in One Dimension
  9. 6. Convergence of Fitted Mesh Finite Difference Methods for Linear Reaction-Diffusion Problems in One Dimension
  10. 7. Properties of Upwind Finite Difference Operators on Piecewise Uniform Fitted Meshes
  11. 8. Convergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in One Dimension
  12. 9. Fitted Mesh Finite Element Methods for Linear Convection-Diffusion Problems in One Dimension
  13. 10. Convergence of Schwarz Iterative Methods for Fitted Mesh Methods in One Dimension
  14. 11. Linear Convection-Diffusion Problems in Two Dimensions and Their Numerical Solution
  15. 12. Bounds on the Derivatives of Solutions of Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary Layers
  16. 13. Convergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary Layers
  17. 14. Limitations of Fitted Operator Methods on Uniform Rectangular Meshes for Problems with Parabolic Boundary Layers
  18. 15. Fitted Numerical Methods for Problems with Initial and Parabolic Boundary Layers
  19. Appendix A Some a priori Bounds for Differential Equations in Two Dimensions
  20. Bibliography
  21. Index