Fitted numerical methods for singular perturbation problems : error estimates in the maximum norm for linear problems in one and two dimensions /
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 revi...
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| Main Author: | |
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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; Hackensack, N.J. :
World Scientific,
©2012.
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| Edition: | Rev. ed. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- 1. Motivation for the study of singular perturbation problems
- 2. Simple examples of singular perturbation problems
- 3. Numerical methods for singular perturbation problems
- 4. Simple fitted operator methods in one dimension
- 5. Simple fitted mesh methods in one dimension
- 6. Convergence of fitted mesh finite difference methods for linear reaction-diffusion problems in one dimension
- 7. Properties of upwind finite difference operators on piecewise uniform fitted meshes
- 8. Convergence of fitted mesh finite difference methods for linear convection-diffusion problems in one dimension
- 9. Fitted mesh finite element methods for linear convection-diffusion problems in one dimension
- 10. Convergence of Schwarz iterative methods for fitted mesh methods in one dimension
- 11. Linear convection-diffusion problems in two dimensions and their numerical solution
- 12. Bounds on the derivatives of solutions of linear convection-diffusion problems in two dimensions with regular boundary layers
- 13. Convergence of fitted mesh finite difference methods for linear convection-diffusion problems in two dimensions with regular boundary layers
- 14. Limitations of fitted operator methods on uniform rectangular meshes for problems with parabolic boundary layers
- 15. Fitted numerical methods for problems with initial and parabolic boundary layers.
