عنوان

Numerical analysis of partial differential equations

شابک

9780470647288 (hardback)

کد کشور

IR

شماره

E-6113

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

کشور محل نشر

IR

عنوان اصلي

Numerical analysis of partial differential equations

نام عام مواد

[Book]

نام نخستين پديدآور

/ S.H. Lui

محل نشرو پخش و غیره

Hoboken, N.J.

نام ناشر، پخش کننده و غيره

: Wiley,

تاریخ نشرو بخش و غیره

, c2011.

نام خاص و کميت اثر

xiii, 487 p. , ill. , 27 cm.

عنوان فروست

(Pure and applied mathematics

ساير اطلاعات عنواني

: a Wiley series of texts, monographs, and tracts.)

متن يادداشت

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.

متن يادداشت

Print

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

متن يادداشت

"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.

عنوان

Pure and applied mathematics (John Wiley & Sons : Unnumbered)

موضوع مستند نشده

Differential equations, Partial, Numerical solutions

شماره

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Lui, S. H.(Shaun H.),1961-

کشور

ایران

وضعیت فهرست نویسی

old catalog

فرمت انتشار

p

نوع ماده

BL

پیشوند ISBD اعمال شده است

1

سطح دسترسي

a

تكميل شده

Y