Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations.

Intro -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.