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 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.

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.