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.
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