LEADER 04476nam 2200661 a 450 001 9910963402703321 005 20251117095439.0 010 $a9789814390743 010 $a9814390747 035 $a(CKB)2550000000101593 035 $a(EBL)919099 035 $a(OCoLC)794328394 035 $a(SSID)ssj0000655965 035 $a(PQKBManifestationID)12237692 035 $a(PQKBTitleCode)TC0000655965 035 $a(PQKBWorkID)10631486 035 $a(PQKB)10502892 035 $a(MiAaPQ)EBC919099 035 $a(WSP)00002674 035 $a(Au-PeEL)EBL919099 035 $a(CaPaEBR)ebr10563505 035 $a(CaONFJC)MIL505490 035 $a(Perlego)847311 035 $a(EXLCZ)992550000000101593 100 $a19960509d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFitted numerical methods for singular perturbation problems $eerror estimates in the maximum norm for linear problems in one and two dimensions /$fJ.J.H. Miller, E. O'Riordan, G.I. Shishkin 205 $aRev. ed. 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$d2012 215 $a1 online resource (191 p.) 300 $aDescription based upon print version of record. 311 08$a9789814390736 311 08$a9814390739 320 $aIncludes bibliographical references and index. 327 $aPreface; Notation, Terminology and Acknowledgments; Contents; 1. Motivation for the Study of Singular Perturbation Problems; 2. Simple Examples of Singular Perturbation Problems; Linear reaction-diffusion equation; Linear convection-diffusion equation; Burger's equation; 3. Numerical Methods for Singular Perturbation Problems; 4. Simple Fitted Operator Methods in One Dimension; 5. Simple Fitted Mesh Methods in One Dimension; 6. Convergence of Fitted Mesh Finite Difference Methods for Linear Reaction-Diffusion Problems in One Dimension 327 $a7. Properties of Upwind Finite Difference Operators on Piecewise Uniform Fitted Meshes8. Convergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in One Dimension; 9. Fitted Mesh Finite Element Methods for Linear Convection-Diffusion Problems in One Dimension; 10. Convergence of Schwarz Iterative Methods for Fitted Mesh Methods in One Dimension; 11. Linear Convection-Diffusion Problems in Two Dimensions and Their Numerical Solution; Linear convection-diffusion problem with regular boundary layers 327 $aLinear convection-diffusion problem with regular and parabolic boundary layersLinear convection-diffusion equation with degenerate parabolic boundary layers; 12. Bounds on the Derivatives of Solutions of Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary Layers; 13. Convergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary Layers; 14. Limitations of Fitted Operator Methods on Uniform Rectangular Meshes for Problems with Parabolic Boundary Layers 327 $a15. Fitted Numerical Methods for Problems with Initial and Parabolic Boundary LayersAppendix A Some a priori Bounds for Differential Equations in Two Dimensions; Bibliography; Index 330 $aSince the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global erro 606 $aDifferential equations$xNumerical solutions 606 $aPerturbation (Mathematics) 615 0$aDifferential equations$xNumerical solutions. 615 0$aPerturbation (Mathematics) 676 $a518 700 $aMiller$b J. J. H$g(John James Henry),$f1937-$0206035 701 $aO'Riordan$b E$g(Eugene)$01864135 701 $aShishkin$b G. I$01864136 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910963402703321 996 $aFitted numerical methods for singular perturbation problems$94470868 997 $aUNINA