03652nam 2200625 450 991081274810332120170816143339.01-4704-0287-4(CKB)3360000000464880(EBL)3114583(SSID)ssj0000973480(PQKBManifestationID)11504621(PQKBTitleCode)TC0000973480(PQKBWorkID)10959051(PQKB)11094876(MiAaPQ)EBC3114583(RPAM)11949243(PPN)195415817(EXLCZ)99336000000046488020000322h20002000 uy| 0engur|n|---|||||txtccrEstimating the error of numerical solutions of systems of reaction-diffusion equations /Donald J. Estep, Mats G. Larson, Roy D. WilliamsProvidence, Rhode Island :American Mathematical Society,[2000]©20001 online resource (125 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 696"July 2000, volume 146, number 696 (end of volume)."0-8218-2072-9 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;no. 696.Reaction-diffusion equationsNumerical calculationsError analysis (Mathematics)Reaction-diffusion equations.Numerical calculations.Error analysis (Mathematics)510 s515/.353Estep Donald J.1959-66935Larson Mats G.1968-Williams Roy D.MiAaPQMiAaPQMiAaPQBOOK9910812748103321Estimating the error of numerical solutions of systems of reaction-diffusion equations4021092UNINA