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Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
List of contents
Introduction.- Polynomial Approximation.- Basic Approaches to Constructing Spectral Methods.- Algebraic Systems and Solution Techniques.- Basic Approaches to Constructing Spectral Methods.- Algebraic Systems and Solution Techniques.- Global Approximation Results.- Theory of Stability and Convergence for Spectral Methods.- Analysis of Model Boundary-Value Problems.- Appendices A-E.
About the author
The authors are among the leading researchers in the field of computational fluid dynamics and have pioneered and promoted the "Spectral Methods in Fluid Dynamics".
Summary
The authors who pioneered Spectral Methods in Fluid Dynamics Calculations in 1988 have now incorporated the many improvements in the algorithms and the theory of spectral methods made since then into this new edition. This improved book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded, as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms. In short, this book provides the most comprehensive, up-to-date theory and state-of-the-art algorithms of spectral methods written by the authors who pioneered the subject.
Additional text
From the reviews:
"The main aim of the book is to discuss the approximations of solutions to ordinary and partial differential equations in single domains by expansions in smooth, global basis functions. … furnishes a comprehensive discussion of the mathematical theory of spectral methods in single domains … . All chapters are enhanced with material on Galerkin method … . The discussion of direct and iterative solution methods is endowed with numerical examples that illustrate the key properties of various spectral approximations and solution algorithms." (Nina Shokina, Zentralblatt MATH, Vol. 1093 (19), 2006)
