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008			240724s2000 xx o ||||0 eng d
020			_a9781470402877 _q(electronic bk.)
020			_z9780821820728
035			_a(MiAaPQ)EBC3114583
035			_a(Au-PeEL)EBL3114583
035			_a(CaPaEBR)ebr11041361
035			_a(OCoLC)922965016
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA377 -- .E88 2000eb
082	0		_a510 s;515/.353
100	1		_aEstep, Donald J.
245	1	0	_aEstimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2000.
264		4	_c©2000.
300			_a1 online resource (125 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.146
505	0		_aIntro -- 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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aReaction-diffusion equations.
650		0	_aNumerical calculations.
650		0	_aError analysis (Mathematics).
655		4	_aElectronic books.
700	1		_aLarson, Mats G.
700	1		_aWilliams, Roy D.
776	0	8	_iPrint version: _aEstep, Donald J. _tEstimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations _dProvidence : American Mathematical Society,c2000 _z9780821820728
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114583 _zClick to View
999			_c70078 _d70078