Chebyshev And Fourier Spectral Methods

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Chebyshev And Fourier Spectral Methods

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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05

Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.

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

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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2001-12-03

Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-03 with Mathematics categories.

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 Fourier Spectral Methods

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Author : John P. Boyd
language : en
Publisher: Springer
Release Date : 1989-09-15

Chebyshev Fourier Spectral Methods written by John P. Boyd and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-15 with Mathematics categories.

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.

Chebyshev Fourier Spectral Methods

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Author : John P. Boyd
language : en
Publisher: Springer
Release Date : 1989

Chebyshev Fourier Spectral Methods written by John P. Boyd and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Technology & Engineering categories.

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.

Mathematics And The Aesthetic

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Author : Nathalie Sinclair
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-28

Mathematics And The Aesthetic written by Nathalie Sinclair and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-28 with Mathematics categories.

A majority of the chapters in this book first saw the light of day as talks at a conference organised and held at Queen’s University in Kingston, Ontario, Canada in April 2001. This small, invitational meeting, tellingly entitled Beauty and the Mathematical Beast, brought together a range of academics int- ested in and committed to exploring connections between mathematics and aesthetics. The enthusiastic response of participants at this gathering enco- aged the presenters to expand upon their initial contributions and persuaded the organisers to recruit further chapters in order to bring a greater balance to the whole. The timing of this event was not arbitrary. The preceding decade had seen a resurgence in serious writing dealing with deeper relations between mathematics (and science) and ‘the beautiful’. In many ways, we the editors of this volume found these contributions to the literature were revisiting and drawing on themes that had been prominent over two thousand five h- dred years ago, in certain writings of the Pythagoreans. While not intending to offer a historical reappraisal of these ancient thinkers here, we have none the less chosen to invoke this profound interweaving of the mathematical and the aesthetic to which this reputedly secretive philosophical sect was ext- sively attuned. This book is divided into three sections comprising three chapters each, each with its own short introduction discussing the particular chapters within.

Spectral Methods In Matlab

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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2000-07-01

Spectral Methods In Matlab written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-01 with Mathematics categories.

Mathematics of Computing -- Numerical Analysis.

Spectral And High Order Methods With Applications

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Author : Jie Shen
language : zh-CN
Publisher:
Release Date : 2006

Spectral And High Order Methods With Applications written by Jie Shen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Calculus categories.

中国科学院科学出版基金资助出版。

Spectral Methods

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Author : Jie Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-25

Spectral Methods written by Jie Shen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.

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.

Spectral Methods And Their Applications

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Author : Ben-yu Guo
language : en
Publisher: World Scientific
Release Date : 1998-05-05

Spectral Methods And Their Applications written by Ben-yu Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-05 with Mathematics categories.

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.