LEADER 05244nam 2200661Ia 450 001 9910877551403321 005 20200520144314.0 010 $a1-283-28277-1 010 $a9786613282774 010 $a1-118-11111-7 010 $a1-118-11113-3 010 $a1-118-11110-9 035 $a(CKB)2550000000054282 035 $a(EBL)693265 035 $a(SSID)ssj0000555232 035 $a(PQKBManifestationID)11366531 035 $a(PQKBTitleCode)TC0000555232 035 $a(PQKBWorkID)10520271 035 $a(PQKB)10558043 035 $a(MiAaPQ)EBC693265 035 $a(OCoLC)757486960 035 $a(PPN)18506065X 035 $a(EXLCZ)992550000000054282 100 $a20110516d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNumerical analysis of partial differential equations /$fS.H. Lui 210 $aHoboken, N.J. $cWiley$dc2011 215 $a1 online resource (508 p.) 225 1 $aPure and applied mathematics : a Wiley series of texts, monographs, and tracts 300 $aDescription based upon print version of record. 311 $a0-470-64728-0 320 $aIncludes bibliographical references and index. 327 $aNumerical Analysis of Partial Differential Equations; Contents; Preface; Acknowledgments; 1 Finite Difference; 1.1 Second-Order Approximation for ?; 1.2 Fourth-Order Approximation for ?; 1.3 Neumann Boundary Condition; 1.4 Polar Coordinates; 1.5 Curved Boundary; 1.6 Difference Approximation for ?2; 1.7 A Convection-Diffusion Equation; 1.8 Appendix: Analysis of Discrete Operators; 1.9 Summary and Exercises; 2 Mathematical Theory of Elliptic PDEs; 2.1 Function Spaces; 2.2 Derivatives; 2.3 Sobolev Spaces; 2.4 Sobolev Embedding Theory; 2.5 Traces; 2.6 Negative Sobolev Spaces 327 $a2.7 Some Inequalities and Identities2.8 Weak Solutions; 2.9 Linear Elliptic PDEs; 2.10 Appendix: Some Definitions and Theorems; 2.11 Summary and Exercises; 3 Finite Elements; 3.1 Approximate Methods of Solution; 3.2 Finite Elements in 1D; 3.3 Finite Elements in 2D; 3.4 Inverse Estimate; 3.5 L2 and Negative-Norm Estimates; 3.6 Higher-Order Elements; 3.7 A Posteriori Estimate; 3.8 Quadrilateral Elements; 3.9 Numerical Integration; 3.10 Stokes Problem; 3.11 Linear Elasticity; 3.12 Summary and Exercises; 4 Numerical Linear Algebra; 4.1 Condition Number; 4.2 Classical Iterative Methods 327 $a4.3 Krylov Subspace Methods4.4 Direct Methods; 4.5 Preconditioning; 4.6 Appendix: Chebyshev Polynomials; 4.7 Summary and Exercises; 5 Spectral Methods; 5.1 Trigonometric Polynomials; 5.2 Fourier Spectral Method; 5.3 Orthogonal Polynomials; 5.4 Spectral Galerkin and Spectral Tau Methods; 5.5 Spectral Collocation; 5.6 Polar Coordinates; 5.7 Neumann Problems; 5.8 Fourth-Order PDEs; 5.9 Summary and Exercises; 6 Evolutionary PDEs; 6.1 Finite Difference Schemes for Heat Equation; 6.2 Other Time Discretization Schemes; 6.3 Convection-Dominated equations; 6.4 Finite Element Scheme for Heat Equation 327 $a6.5 Spectral Collocation for Heat Equation6.6 Finite Difference Scheme for Wave Equation; 6.7 Dispersion; 6.8 Summary and Exercises; 7 Multigrid; 7.1 Introduction; 7.2 Two-Grid Method; 7.3 Practical Multigrid Algorithms; 7.4 Finite Element Multigrid; 7.5 Summary and Exercises; 8 Domain Decomposition; 8.1 Overlapping Schwarz Methods; 8.2 Orthogonal Projections; 8.3 Non-overlapping Schwarz Method; 8.4 Substructuring Methods; 8.5 Optimal Substructuring Methods; 8.6 Summary and Exercises; 9 Infinite Domains; 9.1 Absorbing Boundary Conditions; 9.2 Dirichlet-Neumann Map; 9.3 Perfectly Matched Layer 327 $a9.4 Boundary Integral Methods9.5 Fast Multipole Method; 9.6 Summary and Exercises; 10 Nonlinear Problems; 10.1 Newton's Method; 10.2 Other Methods; 10.3 Some Nonlinear Problems; 10.4 Software; 10.5 Program Verification; 10.6 Summary and Exercises; Answers to Selected Exercises; References; Index 330 $aA balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the num 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aDifferential equations, Partial$xNumerical solutions 606 $aVariational inequalities (Mathematics) 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aVariational inequalities (Mathematics) 676 $a518.64 676 $a518/.64 686 $aMAT034000$2bisacsh 700 $aLui$b S. H$g(Shaun H.),$f1961-$01759115 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877551403321 996 $aNumerical analysis of partial differential equations$94197478 997 $aUNINA