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

• Record Nr.: UNINA9910812748103321
• Autore: Estep Donald J. <1959->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2000]; ©2000
• ISBN: 1-4704-0287-4
• Descrizione fisica: 1 online resource (125 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 696
• Disciplina: 510 s; 515/.353
• Soggetti: Reaction-diffusion equations; Numerical calculations; Error analysis (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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""