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Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams



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Autore: Estep Donald J. <1959-> Visualizza persona
Titolo: Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams Visualizza cluster
Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2000]
©2000
Descrizione fisica: 1 online resource (125 p.)
Disciplina: 510 s
515/.353
Soggetto topico: Reaction-diffusion equations
Numerical calculations
Error analysis (Mathematics)
Soggetto genere / forma: Electronic books.
Persona (resp. second.): LarsonMats G. <1968->
WilliamsRoy D.
Note generali: "July 2000, volume 146, number 696 (end of volume)."
Nota di bibliografia: Includes bibliographical references.
Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""1.1. Numerical analysis and reaction-diffusion equations""; ""1.2. The limitations of classic a priori error analysis""; ""1.3. What we do and don't do in this paper""; ""1.4. A brief overview of related work""; ""1.5. The plan of the paper""; ""Acknowledgments""; ""Chapter 2. A framework for a posteriori error estimation""; ""2.1. The continuous problem and its discretization""; ""2.2. The residual error""; ""2.3. The dual problem and a formula for the error""; ""2.4. The stability factors and the a posteriori error estimate""
""Chapter 3. The size of the residual errors and stability factors""""3.1. The size of the residual errors""; ""3.2. The size of the stability factors""; ""3.3. Application of the analysis to systems with constant diffusion""; ""3.4. The a posteriori estimate and convergence""; ""Chapter 4. Computational error estimation""; ""4.1. Two examples and a stability factor gallery""; ""4.2. Choosing data for the dual problem""; ""4.3. Linearization and the approximate dual problem""; ""4.4. A test of the accuracy and reliability of the error estimate""; ""4.5. Some details of implementation""
""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography""
Titolo autorizzato: Estimating the error of numerical solutions of systems of reaction-diffusion equations  Visualizza cluster
ISBN: 1-4704-0287-4
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910480413403321
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Serie: Memoirs of the American Mathematical Society ; ; no. 696.