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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
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910480413403321 |
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788841503321 |
|
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910812748103321 |
|
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||