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Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486411834
Category : Mathematics
Languages : en
Pages : 690
Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486411834
Category : Mathematics
Languages : en
Pages : 690
Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Category : Mathematics
Languages : en
Pages : 688
Book Description
Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Chebyshev & Fourier Spectral Methods

Chebyshev & Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 798
Book Description
This book is a comprehensive introduction to spectral methods for solving differential equations. Although spectral methods are one of the three main families of numerical algorithms, this book is special in that it is one of only two books published in the last twenty years, which are devoted solely to spectral methods. Spectral methods are now used in such diverse areas as mechanical engineering, numerical weather prediction, ocean modelling, air pollution, aerospace engineering, nonlinear waves, and quantum physics and chemistry.

Chebyshev & Fourier Spectral Methods

Chebyshev & Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Springer
ISBN: 9783642838767
Category : Technology & Engineering
Languages : en
Pages : 0
Book Description
The goal of this book is to teach spectral methods for solving boundary value, eigenvalue, and time-dependent problems. Although the title speaks only of Chebyshev polynomials and trigonometric functions, the book also discusses Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions. These notes evolved from a course I have taught the past five years to an audience drawn from half a dozen different disciplines at the University of Michigan: aerospace engineering, meteorology, physical oceanography, mechanical engineering, naval architecture, and nuclear engineering. With such a diverse audience, this book is not focused on a particular discipline, but rather upon solving differential equations in general. The style is not lemma-theorem-Sobolev space, but algorithms guidelines-rules-of-thumb. Although the course is aimed at graduate students, the required background is limited. It helps if the reader has taken an elementary course in computer methods and also has been exposed to Fourier series and complex variables at the undergraduate level. However, even this background is not absolutely necessary. Chapters 2 to 5 are a self contained treatment of basic convergence and interpolation theory.

Spectral Methods and Their Applications

Spectral Methods and Their Applications PDF Author: Benyu Guo
Publisher: World Scientific
ISBN: 9789810233334
Category : Mathematics
Languages : en
Pages : 364
Book Description
This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.

Spectral Methods

Spectral Methods PDF Author: Claudio Canuto
Publisher: Springer Science & Business Media
ISBN: 3540307265
Category : Science
Languages : en
Pages : 581
Book Description
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

Spectral Methods for Time-Dependent Problems

Spectral Methods for Time-Dependent Problems PDF Author: Jan S. Hesthaven
Publisher: Cambridge University Press
ISBN: 113945952X
Category : Mathematics
Languages : en
Pages :
Book Description
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.

Partial Differential Equations with Numerical Methods

Partial Differential Equations with Numerical Methods PDF Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 3540887059
Category : Mathematics
Languages : en
Pages : 263
Book Description
The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Spectral Methods for Incompressible Viscous Flow

Spectral Methods for Incompressible Viscous Flow PDF Author: Roger Peyret
Publisher: Springer Science & Business Media
ISBN: 1475765576
Category : Mathematics
Languages : en
Pages : 434
Book Description
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.

Spectral Methods

Spectral Methods PDF Author: Jie Shen
Publisher: Springer Science & Business Media
ISBN: 3540710418
Category : Mathematics
Languages : en
Pages : 472
Book Description
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.