MATLAB中的谱方法

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

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

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.