谱方法和高精度算法及其应用

出版时间：2006-12  出版社：科学出版社发行部  作者：本社  页数：326  字数：399000  
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内容概要

　　《谱方法和高精度算法及其应用（英文）》是作者多年教学与科研工作的总结，曾经在香港中文大学，香港浸会大学，加拿大和中国科学院给研究生使用过。主要介绍一些高精度的计算方法，以及相关的程序设计。《谱方法和高精度算法及其应用（英文）》共分5章，第一章主要介绍准谱方法，第二章介绍时态离散和FFT，第三章介绍2D中的谱方法，第四章介绍迭代法和第五章主要是应用程序设计。

书籍目录

Chapter 1 Preliminaries　1.1 Some basic ideas of spectral methods　1.2 Orthogonal polynomials 　1.3 Chebyshev and Legendre polynomials　1.4 Jacobi polynomials and generalized Jacobi polynomials　1.5 Fast Fourier transform　1.6 Several popular time discretization methods 　1.7 Iterative methods and preconditioning　1.8 Error estimates of polynomial approximationsChapter 2 Spectral-Collocation Methods　2.1 Differentiation matrices for polynomial basis functions 　2.2 Differentiation matrices for Fourier collocation methods　2.3 Eigenvalues of Chebyshev collocation operators 　2.4 Chebyshev collocation method for two-point BVPs  　2.5 Collocation method in the weak form and preconditioning  Chapter 3 Spectral-Galerkin Methods　3.1 General setup　3.2  Legendre-Galerkin method　3.3  Chebyshev-Galerkin method　3.4 Chebyshev-Legendre Galerkin method　3.5 Preconditioned iterative method　3.6 Spectral-Galerkin methods for higher-order equations　3.7 Error estimatesChapter 4 Spectral Methods in Unbounded Domains 　4.1 Hermite spectral methods　4.2 Laguerre spectral methods 　4.3 Spectral methods using rational functions  　4.4 Error estimates in unbounded domainsChapter 5 Some applications in one space dimension　5.1 Pseudospectral methods for boundary layer problems　5.2 Pseudospectral methods for Fredholm integral equations　5.3 Chebyshev spectral methods for parabolic equations　5.4 Fourier spectral methods for the KdV equation　5.5 Fourier method and filters　5.6 Essentially non-oscillatory spectral schemesChapter 6 Spectral methods in Multi-dimensional Domains　6.1 Spectral-collocation methods in rectangular domains　6.2 Spectral-Galerkin methods in rectangular domains　6.3 Spectral-Galerkin methods in cylindricaldomains 　6.4 A fast Poisson Solver using finite differencesChapter 7 Some applications in multi-dimensions　7.1 Spectral methods for wave equations　7.2 Laguerre-Hermite method for Schrödinger equations　7.3 Spectral approximation of the Stokes equations　7.4 Spectral-projection method for Navier-Stokes equations　7.5 Axisymmetric flows in a cylinderAppendix A Some online software　A.1 MATLAB Differentiation Matrix Suite　A.2 PseudoPackBibliographyIndex

编辑推荐

　　《谱方法和高精度算法及其应用（英文）》对一些新的科学计算法通过深入浅出的方法作了系统的介绍，并着重培养学生对程序设计的兴趣。　　This book expands lectur enotes by the authors taught in the past few years in USA， Canada and China．The overall emphasis of these notes is to present basic algorithms together with some applications of spectral methods．The aim is to provide a sufficient background on the implementation and analysis of spectral and high-order methods so that the readers can approach the current research literature with the necessary tools and understanding．　　It is expected that this book will be a useful supplement for people studying spectral methods on their own．This book iS especially suited to students interested in high-order methods for PDEs．but it will appeal to numerical analysis and mathematically oriented students and researchers in engineering，physics，and related areas．

用户评论 (总计5条)

•   谱方法虽然不是主流算法，但是本书写的相当好，给出了很多实例，包括非线性波动方程如KdV、NLS方程的谱方法算法和程序，最出色在于书中程序可在网上（***.math.hkbu.edu.hk/~ttang/PGteaching）下载，很方便。
•   通俗易懂，谱方法入门的好书
•   很多研究生课都用这本书，经典。
•   内容还可以，不过里面小错误有点多。。。（沈捷的网页上有些纠错和matlab程序）
•   正在读，但是书里面的错误不少，看的时候必须得仔细。建议多个人一起读，否则有些问题就白白过去了。