08128cam a22006494a 4500 ocn712125079 OCoLC 20171023133843.0 110516s2011 njua b 001 0 eng 2011013570 9780470647288 (hardback) 0470647280 (hardback) 9781118111109 1118111109 9781118111116 1118111117 9781118111130 1118111133 AU@ 000047031659 CHBIS 009756480 CHDSB 005948188 CHVBK 123432669 CHVBK 197627552 DEBBG BV039700484 HEBIS 268594643 (OCoLC)712125079 DLC eng DLC YDX BTCTA YDXCP BWX XII CDX IG# DEBBG BDX OCLCF OCLCQ DXU OCLCQ pcc MAIN QA377 .L84 2011 518/.64 23 MAT034000 bisacsh SK 540 rvk SK 520 rvk Lui, S. H. (Shaun H.), 1961- Numerical analysis of partial differential equations / S.H. Lui. [electronic resource] Hoboken, N.J. : Wiley, �2011. xiii, 487 pages : illustrations ; 27 cm. text txt rdacontent unmediated n rdamedia volume nc rdacarrier Pure and applied mathematics : a Wiley series of texts, monographs, and tracts Machine generated contents note: Preface. Acknowledgments. 1. Finite Difference. 1.1 Second-Order Approximation for [delta].1.2 Fourth-Order Approximation for [delta].1.3 Neumann Boundary Condition. 1.4 Polar Coordinates. 1.5 Curved Boundary. 1.6 Difference Approximation for [delta]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. 2.7 Some Inequalities and Identities. 2.8 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 A Posteriori Estimate. 3.7 Higher-Order Elements. 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 Numbers. 4.2 Classical Iterative Methods. 4.3 Krylov Subspace Methods. 4.4 Preconditioning. 4.5 Direct Methods. 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 Gakerkin and Spectral Tau Methods. 5.5 Spectral Collocation. 5.6 Polar Coordinates. 5.7 Neumann Problems5.8 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. 6.5 Spectral Collocation for Heat Equation. 6.6 Finite Different 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 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. 9.4 Boundary Integral Methods. 9.5 Fast Multiple 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. Includes bibliographical references and index. Preface. Acknowledgments -- Finite Difference. -- Second-Order Approximation for [delta] -- Fourth-Order Approximation for [delta] -- Neumann Boundary Condition -- Polar Coordinates -- Curved Boundary -- Difference Approximation for [delta] -- A Convection-Diffusion Equation -- Appendix: Analysis of Discrete Operators -- Summary and Exercises -- Mathematical Theory of Elliptic PDEs -- Function Spaces -- Derivatives -- Sobolev Spaces -- Sobolev Embedding Theory -- Traces -- Negative Sobolev Spaces -- Some Inequalities and Identities -- Weak Solutions -- Linear Elliptic PDEs -- Appendix: Some Definitions and Theorems -- Summary and Exercises -- Finite Elements. 3.1 Approximate Methods of Solution -- Finite Elements in 1D -- Finite Elements in 2D -- Inverse Estimate -- L2 and Negative-Norm Estimates -- A Posteriori Estimate -- Higher-Order Elements -- Quadrilateral Elements -- Numerical Integration -- Stokes Problem -- Linear Elasticity -- Summary and Exercises -- Numerical Linear Algebra -- Condition Numbers -- Classical Iterative Methods -- Krylov Subspace Methods -- Preconditioning -- Direct Methods -- Appendix: Chebyshev Polynomials -- Summary and Exercises -- Spectral Methods -- Trigonometric Polynomials -- Fourier Spectral Method -- Orthogonal Polynomials -- Spectral Gakerkin and Spectral Tau Methods -- Spectral Collocation -- Polar Coordinates -- Neumann Problems -- Fourth-Order PDEs -- Summary and Exercises -- Evolutionary PDEs -- Finite Difference Schemes for Heat Equation -- Other Time Discretization Schemes -- Convection-Dominated equations -- Finite Element Scheme for Heat Equation -- Spectral Collocation for Heat Equation -- Finite Different Scheme for Wave Equation -- Dispersion -- Summary and Exercises -- Multigrid -- Introduction -- Two-Grid Method -- Practical Multigrid Algorithms -- Finite Element Multigrid -- Summary and Exercises -- Domain Decomposition -- Overlapping Schwarz Methods -- Projections -- Non-overlapping Schwarz Method -- Substructuring Methods -- Optimal Substructuring Methods -- Summary and Exercises -- Infinite Domains -- Absorbing Boundary Conditions -- Dirichlet-Neumann Map -- Perfectly Matched Layer -- Boundary Integral Methods -- Fast Multiple Method -- Summary and Exercises -- Nonlinear Problems -- Newton's Method -- Other Methods -- Some Nonlinear Problems -- Software -- Program Verification -- Summary and Exercises. Answers to Selected Exercises. References. Index. "This book provides a comprehensive and self-contained treatment of the numerical methods used to solve partial differential equations (PDEs), as well as both the error and efficiency of the presented methods. Featuring a large selection of theoretical examples and exercises, the book presents the main discretization techniques for PDEs, introduces advanced solution techniques, and discusses important nonlinear problems in many fields of science and engineering. It is designed as an applied mathematics text for advanced undergraduate and/or first-year graduate level courses on numerical PDEs"-- Provided by publisher. Differential equations, Partial Numerical solutions. MATHEMATICS Mathematical Analysis. bisacsh Differential equations, Partial Numerical solutions. fast (OCoLC)fst00893488 Numerisches Verfahren. (DE-588)4128130-5 gnd Partielle Differentialgleichung. (DE-588)4044779-0 gnd Numerisches Verfahren. (DE-588c)4128130-5 swd Partielle Differentialgleichung. (DE-588c)4044779-0 swd Pure and applied mathematics (John Wiley & Sons : Unnumbered) Wiley InterScience http://onlinelibrary.wiley.com/book/10.1002/9781118111130 ddc BK 208304 208304