Spectral methods: algorithms, analysis and applications

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a varietyof problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures whichare designed to illustrate various concepts stressed in the book. We will also make available a number of basic matlab codes which will help the readers todevelop their own spectral codes for their specific applications. The analysis in this book is presented in a unified framework using the non-uniformly weighted Sobolev spaces which lead to simplified analysis and moreprecise estimates. The book contains, in particular, efficient spectral algorithms and their error analysis for higher-order differential equations, integral equations, problems in unbounded domains and high-dimensional domains. A set of well structured Matlab codes is available online so the readers can easily modify and expand. INDICE: Introduction. Fourier Spectral Methods for Periodic Problems. Orthogonol Polynomials and Related Approximation Results. Second-Order Two-Point Boundary Value Problems. Integral Equations. High-Order Differential Equations.Problems in Unbounded Domains. Multi-Dimensional Domains. Mathematical Preliminaries. Basic iterative methods. Basic time discretization schemes. Instructions for routines in Matlab.

• ISBN: 978-3-540-71040-0
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 480
• Fecha Publicación: 01/08/2011
• Nº Volúmenes: 1
• Idioma: Inglés