Estimating the error of numerical solutions of systems of reaction diffusion equations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
696 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 146, Number 696 (end of volume) |
| Physical Description: | VIII, 109 S. Ill., graph. Darst. |
| ISBN: | 0821820729 |
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MARC
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| 245 | 1 | 0 | |a Estimating the error of numerical solutions of systems of reaction diffusion equations |c Donald J. Estep ; Mats G. Larson ; Roy D. Williams |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2000 | |
| 300 | |a VIII, 109 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 696 | |
| 500 | |a Volume 146, Number 696 (end of volume) | ||
| 650 | 4 | |a Fehleranalyse - Numerisches Verfahren - Reaktions-Diffusionsgleichung | |
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Record in the Search Index
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Contents
Chapter 1. Introduction \
1.1. Numerical analysis and reaction diffusion equations 1
1.2. The limitations of classic a priori error analysis 5
1.3. What we do and don't do in this paper 8
1.4. A brief overview of related work 14
1.5. The plan of the paper 15
Acknowledgments 1(5
Chapter 2. A framework for a posteriori error estimation 17
2.1. The continuous problem and its discretization 17
2.2. The residual error 20
2.3. The dual problem and a formula for the error 21
2.4. The stability factors and the a posteriori error estimate 25
Chapter 3. The size of the residual errors and stability factors 30
3.1. The size of the residual errors 31
3.2. The size of the stability factors 37
3.3. Application of the analysis to systems with constant diffusion 38
3.4. The a posteriori estimate and convergence 41
Chapter 4. Computational error estimation 42
4.1. Two examples and a stability factor gallery 42
4.2. Choosing data for the dual problem 45
4.3. Linearization and the approximate dual problem 50
4.4. A test of the accuracy and reliability of the error estimate 53
4.5. Some details of implementation 54
4.6. Numerical results for the nine models 60
Chapter 5. Preservation of invariant rectangles under discretization 74
5.1. Invariant rectangles and convergence 75
5.2. Preservation of a "fuzzy" invariant rectangle 77
5.3. Exact preservation of an invariant rectangle 82
Chapter 6. Details of the analysis in Chapter 2 87
Chapter 7. Details of the analysis in Chapter 3 91
Chapter 8. Details of the analysis in Chapter 5 99
Bibliography 106
vii |
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| author | Estep, Donald J. 1959- Larson, Mats G. 1968- Williams, Roy D. |
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| id | DE-604.BV013311747 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T08:01:06Z |
| institution | BVB |
| isbn | 0821820729 |
| language | English |
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| physical | VIII, 109 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | American Math. Soc. |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Estep, Donald J. 1959- Verfasser (DE-588)131521640 aut Estimating the error of numerical solutions of systems of reaction diffusion equations Donald J. Estep ; Mats G. Larson ; Roy D. Williams Providence, RI American Math. Soc. 2000 VIII, 109 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 696 Volume 146, Number 696 (end of volume) Fehleranalyse - Numerisches Verfahren - Reaktions-Diffusionsgleichung Fehleranalyse (DE-588)4016608-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Numerisches Verfahren (DE-588)4128130-5 s Fehleranalyse (DE-588)4016608-9 s DE-604 Larson, Mats G. 1968- Verfasser (DE-588)173402216 aut Williams, Roy D. Verfasser aut American Mathematical Society: Memoirs of the American Mathematical Society 696 (DE-604)BV008000141 696 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009076313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Estep, Donald J. 1959- Larson, Mats G. 1968- Williams, Roy D. Estimating the error of numerical solutions of systems of reaction diffusion equations American Mathematical Society: Memoirs of the American Mathematical Society Fehleranalyse - Numerisches Verfahren - Reaktions-Diffusionsgleichung Fehleranalyse (DE-588)4016608-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd |
| subject_GND | (DE-588)4016608-9 (DE-588)4128130-5 (DE-588)4323967-5 |
| title | Estimating the error of numerical solutions of systems of reaction diffusion equations |
| title_auth | Estimating the error of numerical solutions of systems of reaction diffusion equations |
| title_exact_search | Estimating the error of numerical solutions of systems of reaction diffusion equations |
| title_full | Estimating the error of numerical solutions of systems of reaction diffusion equations Donald J. Estep ; Mats G. Larson ; Roy D. Williams |
| title_fullStr | Estimating the error of numerical solutions of systems of reaction diffusion equations Donald J. Estep ; Mats G. Larson ; Roy D. Williams |
| title_full_unstemmed | Estimating the error of numerical solutions of systems of reaction diffusion equations Donald J. Estep ; Mats G. Larson ; Roy D. Williams |
| title_short | Estimating the error of numerical solutions of systems of reaction diffusion equations |
| title_sort | estimating the error of numerical solutions of systems of reaction diffusion equations |
| topic | Fehleranalyse - Numerisches Verfahren - Reaktions-Diffusionsgleichung Fehleranalyse (DE-588)4016608-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd |
| topic_facet | Fehleranalyse - Numerisches Verfahren - Reaktions-Diffusionsgleichung Fehleranalyse Numerisches Verfahren Reaktions-Diffusionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009076313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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