TY  - GEN
AU  - Shen, Jie
AU  - Tang, Tao
AU  - Wang, Li-Lian
TI  - Spectral methods : algorithms, analysis and applications
T2  - Springer series in computational mathematics
SN  - 9783540710400
AV  - QC20.7.S64 
PY  - 2011///]
CY  - Heidelberg
PB  - Springer Berlin
KW  - Spectral theory (Mathematics)
KW  - Partial differential equations
N1  - 1. Introduction
2. Fourier Spectral Methods for Periodic Problems
3. Orthogonal Polynomials and Related Approximation Results
4. Spectral Methods for Second-Order Two-Point Boundary Value Problems
5. Volterra Integral Equations
6. Higher-Order Differential Equations
7. Unbounded Domains
8. Separable Multi-Dimensional Domains
9. Applications in Multi-Dimensional Domains
N2  - 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.---summary provided by publisher
UR  - https://doi.org/10.1007/978-3-540-71041-7
ER  -