Spectral methods in MATLAB

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作者：Lloyd N. Trefethen著

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ISBN：9787302245049

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简介

简介

　　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.　　

　　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
　　Index
　　

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