Spectral and High-Order Methods with Applications-Mathematics Monograph Series 3

The overall emphasis of the present book is to present some basic and high-order algorithms together with applications to some linear and nonlinear problems that one of frequently encounters in practice. The algorithms in the book are presented in a pseudo code format or with MATLAb or FORTRAN codes that easily write computer routines based on the pseudo codes in any standard computer language. We believe that the readers learn and understand numerical theory and then writing and testing computer implementations of them.

For those interested in the numerical analysis of the spectral methods, we have also provided self-contained error analysis for some basic spectral-Galerkin algorithms presented in the book. Our aim is to provide a sufficient background on the implementation and analysis of spectral and high-order methods so that the readers can approach the current research literature with the necessary tools and understanding.

Preface
Chapter 1 Preliminaries
Chapter 2 Spectral-Collocation Methods
Chapter 3 Spectral-Galerkin Methods
Chapter 4 Spectral Methods in Unbounded Domains
Chapter 5 Some applications in one space dimension
Chapter 6 Spectral methods in Multi-dimensional Domains
Chapter 7 Some applications in multi-dimensions
Appendix A Some online software
Bibliography
Index