LEADER 03655nam 2200625 450 001 9910480413403321 005 20170816143339.0 010 $a1-4704-0287-4 035 $a(CKB)3360000000464880 035 $a(EBL)3114583 035 $a(SSID)ssj0000973480 035 $a(PQKBManifestationID)11504621 035 $a(PQKBTitleCode)TC0000973480 035 $a(PQKBWorkID)10959051 035 $a(PQKB)11094876 035 $a(MiAaPQ)EBC3114583 035 $a(PPN)195415817 035 $a(EXLCZ)993360000000464880 100 $a20000322h20002000 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEstimating the error of numerical solutions of systems of reaction-diffusion equations /$fDonald J. Estep, Mats G. Larson, Roy D. Williams 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2000] 210 4$dİ2000 215 $a1 online resource (125 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 696 300 $a"July 2000, volume 146, number 696 (end of volume)." 311 $a0-8218-2072-9 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 696. 606 $aReaction-diffusion equations 606 $aNumerical calculations 606 $aError analysis (Mathematics) 608 $aElectronic books. 615 0$aReaction-diffusion equations. 615 0$aNumerical calculations. 615 0$aError analysis (Mathematics) 676 $a510 s 676 $a515/.353 700 $aEstep$b Donald J.$f1959-$066935 702 $aLarson$b Mats G.$f1968- 702 $aWilliams$b Roy D. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480413403321 996 $aEstimating the error of numerical solutions of systems of reaction-diffusion equations$91923420 997 $aUNINA