スペクトル法とその応用 Spectral Methods and Their Applications

Guo, Ben-yu

World Scientific Publishing Co Pte Ltd（1998/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 360 p.
• 言語 ENG
• 商品コード 9789810233334
• DDC分類 515.7222

基本説明

"This is a very good textbook for anyone who wants to learn spectral methods, in particular, for postgraduate students in numerical methods for PDEs..." Mathematical Reviews.

Full Description

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.

Contents

Orthogonal approximations in Sobolev spaces; stability and convergence; spectral methods and pseudospectral methods; spectral methods for multi-dimensional and high order problems; mixed spectral methods; combined spectral methods; spectral methods on the spherical surface.