| 000 | 08361cam a22007094a 4500 | ||
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| 001 | ocn712125079 | ||
| 003 | OCoLC | ||
| 005 | 20171224115031.0 | ||
| 008 | 110516s2011 njua b 001 0 eng | ||
| 010 | _a 2011013570 | ||
| 040 |
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| 020 |
_a9780470647288 _q(hardback) |
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| 020 |
_a0470647280 _q(hardback) |
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| 020 | _a9781118111109 | ||
| 020 | _a1118111109 | ||
| 020 | _a9781118111116 | ||
| 020 | _a1118111117 | ||
| 020 | _a9781118111130 | ||
| 020 | _a1118111133 | ||
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| 035 | _a(OCoLC)712125079 | ||
| 042 | _apcc | ||
| 050 | 0 | 0 |
_aQA377 _b.L84 2011 |
| 082 | 0 | 0 |
_a518/.64 _223 |
| 084 |
_aMAT034000 _2bisacsh |
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| 084 |
_aSK 540 _2rvk |
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| 084 |
_aSK 520 _2rvk |
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| 049 | _aMAIN | ||
| 100 | 1 |
_aLui, S. H. _q(Shaun H.), _d1961- |
|
| 245 | 1 | 0 |
_aNumerical analysis of partial differential equations / _cS.H. Lui. |
| 260 |
_aHoboken, N.J. : _bWiley, _c�2011. |
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| 300 |
_axiii, 487 pages : _billustrations ; _c27 cm. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_aunmediated _bn _2rdamedia |
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| 338 |
_avolume _bnc _2rdacarrier |
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| 490 | 1 | _aPure and applied mathematics : a Wiley series of texts, monographs, and tracts | |
| 520 |
_a"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"-- _cProvided by publisher. |
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| 504 | _aIncludes bibliographical references and index. | ||
| 500 | _aMachine 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. | ||
| 505 | 0 | 0 |
_gPreface. Acknowledgments -- _tFinite Difference. -- _tSecond-Order Approximation for [delta] -- _tFourth-Order Approximation for [delta] -- _tNeumann Boundary Condition -- _tPolar Coordinates -- _tCurved Boundary -- _tDifference Approximation for [delta] -- _tA Convection-Diffusion Equation -- _gAppendix: _tAnalysis of Discrete Operators -- _tSummary and Exercises -- _tMathematical Theory of Elliptic PDEs -- _tFunction Spaces -- _tDerivatives -- _tSobolev Spaces -- _tSobolev Embedding Theory -- _tTraces -- _tNegative Sobolev Spaces -- _tSome Inequalities and Identities -- _tWeak Solutions -- _tLinear Elliptic PDEs -- _gAppendix: _tSome Definitions and Theorems -- _gSummary and Exercises -- _tFinite Elements. 3.1 Approximate Methods of Solution -- _tFinite Elements in 1D -- _tFinite Elements in 2D -- _tInverse Estimate -- _tL2 and Negative-Norm Estimates -- _tA Posteriori Estimate -- _tHigher-Order Elements -- _tQuadrilateral Elements -- _tNumerical Integration -- _tStokes Problem -- _tLinear Elasticity -- _gSummary and Exercises -- _tNumerical Linear Algebra -- _tCondition Numbers -- _tClassical Iterative Methods -- _tKrylov Subspace Methods -- _tPreconditioning -- _tDirect Methods -- _gAppendix: _tChebyshev Polynomials -- _gSummary and Exercises -- _tSpectral Methods -- _tTrigonometric Polynomials -- _tFourier Spectral Method -- _tOrthogonal Polynomials -- _tSpectral Gakerkin and Spectral Tau Methods -- _tSpectral Collocation -- _tPolar Coordinates -- _tNeumann Problems -- _tFourth-Order PDEs -- _gSummary and Exercises -- _tEvolutionary PDEs -- _tFinite Difference Schemes for Heat Equation -- _tOther Time Discretization Schemes -- _tConvection-Dominated equations -- _tFinite Element Scheme for Heat Equation -- _tSpectral Collocation for Heat Equation -- _tFinite Different Scheme for Wave Equation -- _tDispersion -- _gSummary and Exercises -- _tMultigrid -- _gIntroduction -- _tTwo-Grid Method -- _tPractical Multigrid Algorithms -- _tFinite Element Multigrid -- _gSummary and Exercises -- _tDomain Decomposition -- _tOverlapping Schwarz Methods -- _tProjections -- _tNon-overlapping Schwarz Method -- _tSubstructuring Methods -- _tOptimal Substructuring Methods -- _gSummary and Exercises -- _tInfinite Domains -- _tAbsorbing Boundary Conditions -- _tDirichlet-Neumann Map -- _tPerfectly Matched Layer -- _tBoundary Integral Methods -- _tFast Multiple Method -- _gSummary and Exercises -- _tNonlinear Problems -- _tNewton's Method -- _tOther Methods -- _tSome Nonlinear Problems -- _tSoftware -- _tProgram Verification -- _gSummary and Exercises. Answers to Selected Exercises. References. Index. |
| 650 | 0 |
_aDifferential equations, Partial _xNumerical solutions. |
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| 650 | 7 |
_aMATHEMATICS _xMathematical Analysis. _2bisacsh |
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| 650 | 7 |
_aDifferential equations, Partial _xNumerical solutions. _2fast _0(OCoLC)fst00893488 |
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| 650 | 0 | 7 |
_aNumerisches Verfahren. _0(DE-588)4128130-5 _2gnd |
| 650 | 0 | 7 |
_aPartielle Differentialgleichung. _0(DE-588)4044779-0 _2gnd |
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_aNumerisches Verfahren. _0(DE-588c)4128130-5 _2swd |
| 650 | 0 | 7 |
_aPartielle Differentialgleichung. _0(DE-588c)4044779-0 _2swd |
| 830 | 0 | _aPure and applied mathematics (John Wiley & Sons : Unnumbered) | |
| 856 | 4 | 0 |
_3Wiley InterScience _uhttp://onlinelibrary.wiley.com/book/10.1002/9781118111130 |
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