Spectral Methods in MATLAB (Software, Environments, Tools) by Trefethen, Lloy…
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Synopsis
Explores spectral methods built around MATLAB programmes. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high-level programming of MATLAB. This hands-on introduction is built around 40 short and powerful MATLAB programmes, which the reader can download from the World Wide Web.This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high-level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.
Product Identifiers
ISBN-10
0898714656
ISBN-13
9780898714654
Key Details
Author
Lloyd N. Trefethen
Number Of Pages
181 pages
Series
Software, Environments, and Tools
Format
EBOOK
Publication Date
2000-01-01
Language
English
Publisher
Society for Industrial and Applied Mathematics
Publication Year
2000
Additional Details
Series Volume Number
Vol. 10
Copyright Date
2000
Illustrated
Yes
Dimensions
Weight
12 Oz
Height
0.4 In.
Width
6 In.
Length
9 In.
Target Audience
Group
Scholarly & Professional
Classification Method
LCCN
00-036559
LC Classification Number
QA377.T65 2000
Dewey Decimal
515/.7222
Dewey Edition
21
Table Of Content
Preface; 1. Differentiation matrices; 2. Unbounded grids: the semidiscrete Fourier transform; 3. Periodic grids: the DFT and FFT; 4. Smoothness and spectral accuracy; 5. Polynomial interpolation and clustered grids; 6. Chebyshev differentiation matrices; 7. Boundary value problems; 8. Chebyshev series and the FFT; 9. Eigenvalues and pseudospectra; 10. Time-stepping and stability regions; 11. Polar coordinates; 12. Integrals and quadrature formulas; 13. More about boundary conditions; 14. Fourth-order problems; Afterword; Bibliography; Index.
Reviews
'A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.' Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan'Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.'Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.'The book's succinct style and the understanding that is gained by parsing and experimenting with MATLAB routines allow for a large number of fundamental concepts to be conveyed in a few pages... I recommend this book highly; it is clear, concise, and dense with interesting and exciting examples. It is an appropriate text for an introductory class on the subject and also includes many ideas and explanations that are appealing to a broader research audience.' SIAM Review'This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.' Chi-Wang Shu, Mathematics of Computation'This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.' David Gottlieb, Brown University'What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].'Peter Mucha, Massachusetts Institute of Technology‘A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.’Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan‘Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.’Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.‘This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.’Chi-Wang Shu, Mathematics of Computation‘This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.’David Gottlieb, Ford Foundation Professor of Applied Mathematics, Brown University‘What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].’Peter Mucha, Massachusetts Institute of Technology�A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.�Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan�Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.�Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.�This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.�Chi-Wang Shu, Mathematics of Computation�This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.�David Gottlieb, Ford Foundation Professor of Applied Mathematics, Brown University�What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].�Peter Mucha, Massachusetts Institute of Technology
Synopsis
Explores spectral methods built around MATLAB programmes. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high-level programming of MATLAB. This hands-on introduction is built around 40 short and powerful MATLAB programmes, which the reader can download from the World Wide Web.This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high-level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.
Product Identifiers
ISBN-10
0898714656
ISBN-13
9780898714654
Key Details
Author
Lloyd N. Trefethen
Number Of Pages
181 pages
Series
Software, Environments, and Tools
Format
EBOOK
Publication Date
2000-01-01
Language
English
Publisher
Society for Industrial and Applied Mathematics
Publication Year
2000
Additional Details
Series Volume Number
Vol. 10
Copyright Date
2000
Illustrated
Yes
Dimensions
Weight
12 Oz
Height
0.4 In.
Width
6 In.
Length
9 In.
Target Audience
Group
Scholarly & Professional
Classification Method
LCCN
00-036559
LC Classification Number
QA377.T65 2000
Dewey Decimal
515/.7222
Dewey Edition
21
Table Of Content
Preface; 1. Differentiation matrices; 2. Unbounded grids: the semidiscrete Fourier transform; 3. Periodic grids: the DFT and FFT; 4. Smoothness and spectral accuracy; 5. Polynomial interpolation and clustered grids; 6. Chebyshev differentiation matrices; 7. Boundary value problems; 8. Chebyshev series and the FFT; 9. Eigenvalues and pseudospectra; 10. Time-stepping and stability regions; 11. Polar coordinates; 12. Integrals and quadrature formulas; 13. More about boundary conditions; 14. Fourth-order problems; Afterword; Bibliography; Index.
Reviews
'A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.' Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan'Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.'Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.'The book's succinct style and the understanding that is gained by parsing and experimenting with MATLAB routines allow for a large number of fundamental concepts to be conveyed in a few pages... I recommend this book highly; it is clear, concise, and dense with interesting and exciting examples. It is an appropriate text for an introductory class on the subject and also includes many ideas and explanations that are appealing to a broader research audience.' SIAM Review'This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.' Chi-Wang Shu, Mathematics of Computation'This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.' David Gottlieb, Brown University'What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].'Peter Mucha, Massachusetts Institute of Technology‘A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.’Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan‘Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.’Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.‘This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.’Chi-Wang Shu, Mathematics of Computation‘This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.’David Gottlieb, Ford Foundation Professor of Applied Mathematics, Brown University‘What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].’Peter Mucha, Massachusetts Institute of Technology�A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.�Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan�Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.�Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.�This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.�Chi-Wang Shu, Mathematics of Computation�This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.�David Gottlieb, Ford Foundation Professor of Applied Mathematics, Brown University�What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].�Peter Mucha, Massachusetts Institute of Technology