Synopses & Reviews
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
Review
From the reviews: "This book provides a self-contained presentation for the construction, implementation and analysis of spectral algorithms for some model equations of elliptic, dispersive and parabolic type. ... a textbook for graduate students in mathematics and other sciences and engineering. ... The book has nine chapters, each of them ending with a small collection of problems." (Julia Novo, Mathematical Reviews, January, 2013) "This is a self-contained presentation on the construction, implementation, and analysis of spectral methods for various differential and integral equations, with wide applications in science and engineering. ... Every chapter ends with a set of problems for practice. ... This excellent and very well-written book could be used as s graduate textbook in mathematics and other engineering disciplines. It would also be a good reference book for active practitioners and researchers of spectral methods." (Srinivasan Natesan, ACM Computing Reviews, January, 2013)
Review
From the reviews:
"This book provides a self-contained presentation for the construction, implementation and analysis of spectral algorithms for some model equations of elliptic, dispersive and parabolic type. ... a textbook for graduate students in mathematics and other sciences and engineering. ... The book has nine chapters, each of them ending with a small collection of problems." (Julia Novo, Mathematical Reviews, January, 2013)
"This is a self-contained presentation on the construction, implementation, and analysis of spectral methods for various differential and integral equations, with wide applications in science and engineering. ... Every chapter ends with a set of problems for practice. ... This excellent and very well-written book could be used as s graduate textbook in mathematics and other engineering disciplines. It would also be a good reference book for active practitioners and researchers of spectral methods." (Srinivasan Natesan, ACM Computing Reviews, January, 2013)
About the Author
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:
Table of Contents
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