Spectral Methods

TRAMA

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 variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

SOMMARIO

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.  

AUTORE

Jie Shen: Ph.D., Numerical Analysis, Universite de Paris-Sud, Orsay, France, 1987; B.S., Computational Mathematics, Peking University, China, 1982. Professor of Mathematics at Purdue University; Guest Professorships in Shanghai University and Xiamen University; Member of editorial boards for numerous top research journals.Tao Tang:  Ph.D., Applied Mathematics, University of Leeds, 1989;Computational Mathematics, Peking University, China, 1984. Head and  Chair Professor of Hong Kong Baptist University; Cheung Kong Chair  Professor under Ministry of Education of China; Winner of a Leslie Fox Prize in 1988 and a Feng Kang Prize in Scientific Computing in  2003; Member of editorial boards for numerous  top research journals.Lilian Wang: Ph.D, Computational Mathematics, Shanghai University, China  2000; B.S., Mathematics Education,  Hunan University of Science and Technology, China, 1995.Assistant Professor of Mathematics,  Nanyang Technological University, Singapore. A  prolific researcher with over twenty research papers in top journals.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9783642270970
• Collana: Springer Series in Computational Mathematics
• Dimensioni: 235 x 155 mm
• Formato: Brossura
• Illustration Notes: XVI, 472 p.
• Pagine Arabe: 472
• Pagine Romane: xvi