Cargando…
Estimating the error of numerical solutions of systems of reaction-diffusion equations /
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2000.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 696. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn851088833 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr un||||||||| | ||
| 008 | 130627s2000 riua ob 000 0 eng d | ||
| 040 | |a GZM |b eng |e pn |c GZM |d OCLCO |d COO |d UIU |d OCLCF |d LLB |d E7B |d OCLCQ |d EBLCP |d YDXCP |d OCLCQ |d AU@ |d UKAHL |d OCLCQ |d LEAUB |d VT2 |d OCLCO |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 908039971 |a 922965016 |a 1086549677 | ||
| 020 | |a 9781470402877 | ||
| 020 | |a 1470402874 | ||
| 020 | |z 9780821820728 | ||
| 020 | |z 0821820729 | ||
| 029 | 1 | |a AU@ |b 000069468038 | |
| 035 | |a (OCoLC)851088833 |z (OCoLC)908039971 |z (OCoLC)922965016 |z (OCoLC)1086549677 | ||
| 050 | 4 | |a QA3 |b .A57 no. 696 |a QA377 | |
| 082 | 0 | 4 | |a 510 s 515/.353 |2 21 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Estep, Donald J., |d 1959- |1 https://id.oclc.org/worldcat/entity/E39PBJrrvwpGjcTYhbXwMCHpyd | |
| 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. |
| 260 | |a Providence, R.I. : |b American Mathematical Society, |c ©2000. | ||
| 300 | |a 1 online resource (viii, 109 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v v. 696 | |
| 500 | |a "July 2000, volume 146, number 696 (end of volume)." | ||
| 504 | |a Includes bibliographical references (106-109). | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization. | |
| 505 | 0 | 0 | |t 1. Introduction |t 2. A framework for a posteriori error estimation |t 3. The size of the residual errors and stability factors |t 4. Computational error estimation |t 5. Preservation of invariant rectangles under discretization |t 6. Details of the analysis in Chapter 2 |t 7. Details of the analysis in Chapter 3 |t 8. Details of the analysis in Chapter 5. |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Reaction-diffusion equations. | |
| 650 | 0 | |a Numerical calculations. | |
| 650 | 0 | |a Error analysis (Mathematics) | |
| 650 | 6 | |a Équations de réaction-diffusion. | |
| 650 | 6 | |a Calculs numériques. | |
| 650 | 6 | |a Théorie des erreurs. | |
| 650 | 7 | |a Error analysis (Mathematics) |2 fast | |
| 650 | 7 | |a Numerical calculations |2 fast | |
| 650 | 7 | |a Reaction-diffusion equations |2 fast | |
| 700 | 1 | |a Larson, Mats G., |d 1968- |1 https://id.oclc.org/worldcat/entity/E39PCjy7VTbjQgmrTxtp4by9Kq | |
| 700 | 1 | |a Williams, Roy D. | |
| 758 | |i has work: |a Estimating the error of numerical solutions of systems of reaction-diffusion equations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGFVQ3kh8QCgdG8YWrRYfq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Estep, Donald J., 1959- |t Estimating the error of numerical solutions of systems of reaction-diffusion equations / |x 0065-9266 |z 9780821820728 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 696. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114583 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH35005945 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL3114583 | ||
| 938 | |a ebrary |b EBRY |n ebr11041361 | ||
| 938 | |a YBP Library Services |b YANK |n 12375412 | ||
| 994 | |a 92 |b IZTAP | ||