譜方法和高精度算法及其應用

內容概要

　　《譜方法和高精度算法及其應用（英文）》是作者多年教學與科研工作的總結，曾經在香港中文大學，香港浸會大學，加拿大和中國科學院給研究生使用過。主要介紹一些高精度的計算方法，以及相關的程序設計?！蹲V方法和高精度算法及其應用（英文）》共分5章，第一章主要介紹準譜方法，第二章介紹時態(tài)離散和FFT，第三章介紹2D中的譜方法，第四章介紹迭代法和第五章主要是應用程序設計。

書籍目錄

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

編輯推薦

　　《譜方法和高精度算法及其應用（英文）》對一些新的科學計算法通過深入淺出的方法作了系統(tǒng)的介紹，并著重培養(yǎng)學生對程序設計的興趣?！　his 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．

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