Chebyshev & Fourier Spectral Methods: 49 (Lecture Notes in Engineering) - Tapa blanda

Boyd, John P. P.

 
9783540514879: Chebyshev & Fourier Spectral Methods: 49 (Lecture Notes in Engineering)

Sinopsis

This book is a comprehensive introduction to spectral methods for solving differential equations. Although spectral methods are one of the three main families of numerical algorithms, this book is special in that it is one of only two books published in t

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Reseña del editor

This book is a comprehensive introduction to spectral methods for solving differential equations. Although spectral methods are one of the three main families of numerical algorithms, this book is special in that it is one of only two books published in t

Reseña del editor

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.

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