MATLAB中的譜方法

內(nèi)容概要

The aim of this book is to teach you the
essentials of spectral collocation methods with the aid of 40 short
MATLAB programs, or "M-files."* The programs are available online
at http://www, comlab, ox. ac .uk/oucl/work/nick.trefethen, and you
will run them and modify them to solve all kinds of ordinary and
partial differential equations (ODEs and PDEs) connected with
problems in fluid mechanics, quantum mechanics, vibrations, linear
and nonlinear waves, complex analysis, and other fields. Concerning
prerequisites,it is assumed that the words just written have
meaning for you, that you have some knowledge of numerical methods,
and that you already know MATLAB.

作者簡介

作者：（美國）特弗森（Lloyd N.Trefethen）Lloyd N.Trefethen is Professor of Numerical Analysis at Oxford University. His previous SIAM book, Numerical Linear Algebra (with David Bau III, 1997) has sold over 5000 copies.

書籍目錄

preface
acknowledgments
a note on the matlab programs
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

章節(jié)摘錄

版權頁：插圖：A number of other colleagues commented upon drafts of the book and improved it. I am especially grateful to John Boyd, Frederic Dias, Des Higham, Nick Higham, Alvaro Meseguer, Paul Milewski, Damian Packer, and Satish Reddy.In a category by himself goes Mark Embree, who has read this book more carefully than anyone else but me, by far. Embree suggested many improvements in the text, and beyond that, he worked many of the exercises, catching errors and contributing new exercises of his own. I am lucky to have found Embree at a stage of his career when he still has so much time to give to others.The Numerical Analysis Group here at Oxford provides a stimulating environment to support a project like this. I want particularly to thank my three close colleagues Mike Giles, Endre Still, and Andy Wathen, whose friendship has made me glad I came to Oxford; Shirley Dickson, who cheerfully made multiple copies of drafts of the text half a dozen times on short notice; and our outstanding group secretary and administrator, Shirley Day, who will forgive me, I hope, for all the mornings I spent working on this book when I should have been doing other things.This book started out as a joint production with Andrew Spratley, a D. Phil. student, based on a masters-level course I taught in 1998 and 1999. I want to thank Spratley for writing the first draft of many of these pages and for major contributions to the book's layout and figures. Without his impetus, the book would not have been written.Once we knew it would be written, there was no doubt who the publisher should be. It was a pleasure to publish my previous book [TrBa97] with SIAM, an organization that manages to combine the highest professional standards with a personal touch. And there was no doubt who the copy editor should be: again the remarkable Beth Gallagher, whose eagle eye and good sense have improved the presentation from beginning to end.

媒體關注與評論

Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.　　——Cleve Moler. Chairman and Chief Scientist, The Mathworks, Inc.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

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