Spectral Methods: Algorithms, Analysis and Applications

From the reviews:

“The text consists of nine main chapters, with the material naturally separating into two groups. … the text does a very good job at outlining the importance of creativity and analysis in the development of modern computational techniques for complex applications. … I read the text with enjoyment and expect it to be of great value as a reference, in particular for its careful presentation of key analytic results, and as a comprehensive introduction to the more detailed exposition of the authors’ work … .” (Jan S. Hesthaven, SIAM Review, Vol. 55 (2), 2013)

“This is a largely self-contained book on major parts of the application of spectral methods to the numerical solution of partial differential equations … . The material is accessible to … advanced students of mathematics and also to researchers in neighbouring fields wishing to acquire a sound knowledge of methods they might intend to apply.” (H. Muthsam, Monatshefte für Mathematik, Vol. 170 (2), May, 2013)

“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)