SPECTRAL METHODS & THEIR APPLICATIONS

By: BEN-YU GUO

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Hardcover | 6 May 1998

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358 Pages

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22.86 x 15.24 x 2.06

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This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.

The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Applied Mathematics Booktopia Publisher Services World Scientific Publishing

Preface
Introduction	p. 1
Orthogonal Approximations in Sobolev Spaces	p. 10
Preliminaries	p. 10
Fourier Approximations	p. 16
Orthogonal Systems of Polynomials in a Finite Interval	p. 24
Legendre Approximations	p. 31
Chebyshev Approximations	p. 43
Some Orthogonal Approximations in Infinite Intervals	p. 56
Filterings and Recovering the Spectral Accuracy	p. 66
Stability and Convergence	p. 82
Stability and Convergence for Linear Problems	p. 82
Generalized Stability for Nonlinear Problems	p. 86
Initial-Value Problems	p. 94
Spectral Methods and Pseudospectral Methods	p. 100
Fourier Spectral Methods and Fourier Pseudospectral Methods	p. 100
Legendre Spectral Methods and Legendre Pseudospectral Methods	p. 120
Chebyshev Spectral Methods and Chebyshev Pseudospectral Methods	p. 143
Spectral Penalty Methods	p. 152
Spectral Vanishing Viscosity Methods	p. 164
Spectral Approximations of Isolated Solutions	p. 181
Spectral Methods for Multi-Dimensional and High Order Problems	p. 188
Orthogonal Approximations in Several Dimensions	p. 188
Spectral Methods for Multi-Dimensional Nonlinear Systems	p. 196
Spectral Methods for Nonlinear High Order Equations	p. 210
Spectral Domain Decomposition Methods	p. 231
Spectral Multigrid Methods	p. 248
Mixed Spectral Methods	p. 257
Mixed Fourier-Legendre Approximations	p. 257
Mixed Fourier-Chebyshev Approximations	p. 265
Applications	p. 273
Combined Spectral Methods	p. 280
Some Basic Results in Finite Element Methods	p. 280
Combined Fourier-Finite Element Approximations	p. 284
Combined Legendre-Finite Element Approximations	p. 289
Combined Chebyshev-Finite Element Approximations	p. 295
Applications	p. 300
Spectral Methods on the Spherical Surface	p. 313
Spectral Approximation on the Spherical Surface	p. 313
Pseudospectral Approximation on the Spherical Surface	p. 318
Applications	p. 322
References	p. 331
Table of Contents provided by Blackwell. All Rights Reserved.

SPECTRAL METHODS & THEIR APPLICATIONS

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